Search results for: semantic differential

Authors: Renukswamy Chikkamath, Vishvapalsinhji Ramsinh Parmar, Christoph Hewel, Markus Endres

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Given a patent document, identifying distinct semantic annotations is an interesting research aspect. Text annotation helps the patent practitioners such as examiners and patent attorneys to quickly identify the key arguments of any invention, successively providing a timely marking of a patent text. In the process of manual patent analysis, to attain better readability, recognising the semantic information by marking paragraphs is in practice. This semantic annotation process is laborious and time-consuming. To alleviate such a problem, we proposed a dataset to train machine learning algorithms to automate the highlighting process. The contributions of this work are: i) we developed a multi-class dataset of size 150k samples by traversing USPTO patents over a decade, ii) articulated statistics and distributions of data using imperative exploratory data analysis, iii) baseline Machine Learning models are developed to utilize the dataset to address patent paragraph highlighting task, and iv) future path to extend this work using Deep Learning and domain-specific pre-trained language models to develop a tool to highlight is provided. This work assists patent practitioners in highlighting semantic information automatically and aids in creating a sustainable and efficient patent analysis using the aptitude of machine learning.

Keywords: machine learning, patents, patent sentiment analysis, patent information retrieval

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Authors: Mohammad Alqahtani, Eric Atwell

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This paper reviews and classifies most of the important types of search techniques that have been applied on the holy Quran. Then, it addresses the limitations in these techniques. Additionally, this paper surveys most existing Quranic ontologies and what are their deficiencies. Finally, it explains a new search tool called: A semantic search tool for Al Quran based on Qur’anic ontologies. This tool will overcome all limitations in the existing Quranic search applications.

Keywords: holy Quran, natural language processing (NLP), semantic search, information retrieval (IR), ontology

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Authors: Jiya Mohammed, Ibrahim Ismail Giwa

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Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables.

Keywords: coupled differential equation, Homotopy Perturbation Method, plates, squeezing flow

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: Farzaneh Badinlou, Reza Kormi-Nouri, Monika Knopf, Kamal Kharazi

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Research into long-term memory has demonstrated that the richness of the knowledge base cues in memory tasks improves retrieval process, which in turn influences learning and memory performance. The present research investigated the idea that adding cues connected to knowledge can affect memory performance in the context of action memory in children. In action memory studies, participants are instructed to learn a series of verb–object phrases as verbal learning and experience-based learning (learning by doing and learning by observation). It is well established that executing action phrases is a more memorable way to learn than verbally repeating the phrases, a finding called enactment effect. In the present study, a total of 410 students from four grade groups—2nd, 4th, 6th, and 8th—participated in this study. During the study, participants listened to verbal action phrases (VTs), performed the phrases (SPTs: subject-performed tasks), and observed the experimenter perform the phrases (EPTs: experimenter-performed tasks). During the test phase, cued recall test was administered. Semantic relational cues (i.e., well-integrated vs. poorly integrated items) were manipulated in the present study. In that, the participants were presented two lists of action phrases with high semantic integration between verb and noun, e.g., “write with the pen” and with low semantic integration between verb and noun, e.g., “pick up the glass”. Results revealed that experience-based learning had a better results than verbal learning for both well-integrated and poorly integrated items, though manipulations of semantic relational cues can moderate the enactment effect. In addition, children of different grade groups outperformed for well- than poorly integrated items, in flavour of older children. The results were discussed in relation to the effect of knowledge-based information in facilitating retrieval process in children.

Keywords: action memory, enactment effect, knowledge-based cues, school-aged children, semantic relational cues

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Authors: Thomas Ousterhout

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In an effort to test the ability of a commercial grade EEG headset to effectively measure the N400 ERP, a replication study was conducted to see if similar results could be produced as that which used a medical grade EEG. Pictures of meaningful and meaningless hand postures were borrowed from the original author and subjects were required to perform a semantic discrimination task. The N400 was detected indicating semantic processing of the meaningfulness of the hand postures. The results corroborate those of the original author and support the use of some commercial grade EEG headsets for non-critical research applications.

Keywords: EEG, ERP, N400, semantics, congruency, gestures, emotiv

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Authors: Aaron Zhang, Alimire Kahaer, Gerald Weber, Nalin Arachchilage

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Access control is an essential safeguard for the security of enterprise data, which controls users’ access to information resources and ensures the confidentiality and integrity of information resources [1]. Research shows that the more common types of access control now have shortcomings [2]. In this direction, to improve the existing access control, we have studied the current technologies in the field of data security, deeply investigated the previous data access control policies and their problems, identified the existing deficiencies, and proposed a new extension structure of SPBAC. SPBAC extension proposed in this paper aims to combine Policy-Based Access Control (PBAC) with semantics to provide logically connected, real-time data access functionality by establishing associations between enterprise data through semantics. Our design combines policies with linked data through semantics to create a "Semantic link" so that access control is no longer per-database and determines that users in each role should be granted access based on the instance policy, and improves the SPBAC implementation by constructing policies and defined attributes through the XACML specification, which is designed to extend on the original XACML model. While providing relevant design solutions, this paper hopes to continue to study the feasibility and subsequent implementation of related work at a later stage.

Keywords: access control, semantic policy-based access control, semantic link, access control model, instance policy, XACML

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Authors: Jessevel Montes

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This study explored on the culture of journal writing among the Senior High School Manobo students. The purpose of this qualitative morpho-semantic and syntactic study was to discover the morphological, semantic, and syntactic features of the written output through morphological, semantic, and syntactic categories present in their journal writings. Also, beliefs and practices embedded in the norms, values, and ideologies were identified. The study was conducted among the Manobo students in the Senior High Schools of Central Mindanao, particularly in the Division of North Cotabato. Findings revealed that morphologically, the features that flourished are the following: subject-verb concordance, tenses, pronouns, prepositions, articles, and the use of adjectives. Semantically, the features are the following: word choice, idiomatic expression, borrowing, and vernacular. Syntactically, the features are the types of sentences according to structure and function; and the dominance of code switching and run-on sentences. Lastly, as to the beliefs and practices embedded in the norms, values, and ideologies of their journal writing, the major themes are: valuing education, family, and friends as treasure, preservation of culture, and emancipation from the bondage of poverty. This study has shed light on the writing capabilities and weaknesses of the Manobo students when it comes to English language. Further, such an insight into language learning problems is useful to teachers because it provides information on common trouble-spots in language learning, which can be used in the preparation of effective teaching materials.

Keywords: applied linguistics, culture, morpho-semantic and syntactic analysis, Manobo Senior High School, Philippines

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz

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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.

Keywords: differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot

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Authors: Ramdas Sonawane, Mahaveer Gadiya

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The control problem associated with nuclear dynamics is represented by nonlinear integro-differential equation with additive controls. To control chain reaction, certain amount of neutrons is added into (or withdrawn out of) chamber as and when required. It is not realistic. So, we can think of controlling the reactor dynamics by bilinear control, which enters the system as coefficient of state. In this paper, we study the approximate and exact controllability of parabolic integro-differential equation controlled by bilinear control with non-homogeneous boundary conditions in bounded domain. We prove the existence of control and propose an explicit control strategy.

Keywords: approximate control, exact control, bilinear control, nuclear dynamics, integro-differential equations

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Authors: K. P. Valdés García, E. I. Rodríguez Fonseca, L. G. Juárez Cantú

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Suicide is a global, multidimensional and dynamic problem of mental health, which requires a constant study for its understanding and prevention. When research of this phenomenon is done, it is necessary to consider the different characteristics it may have because of the individual and sociocultural variables, the importance of this consideration is related to the generation of effective treatments and interventions. Adolescents are a vulnerable population due to the characteristics of the development stage. The investigation was carried out with the objective of identifying and describing the conceptualization of adolescents of suicide, and in this process, we find possible differences between men and women. The study was carried out in Saltillo, Coahuila, Mexico. The sample was composed of 418 volunteer students aged between 11 and 18 years. The ethical aspects of the research were reviewed and considered in all the processes of the investigation with the participants, their parents and the schools to which they belonged, psychological attention was offered to the participants and preventive workshops were carried in the educational institutions. Natural semantic networks were the instrument used, since this hybrid method allows to find and analyze the social concept of a phenomenon; in this case, the word suicide was used as an evocative stimulus and participants were asked to evoke at least five words and a maximum 10 that they thought were related to suicide, and then hierarchize them according to the closeness with the construct. The subsequent analysis was carried with Excel, yielding the semantic weights, affective loads and the distances between each of the semantic fields established according to the words reported by the subjects. The results showed similarities in the conceptualization of suicide in adolescents, men and women. Seven semantic fields were generated; the words were related in the discourse analysis: 1) death, 2) possible triggering factors, 3) associated moods, 4) methods used to carry it out, 5) psychological symptomatology that could affect, 6) words associated with a rejection of suicide, and finally, 7) specific objects to carry it out. One of the necessary aspects to consider in the investigations of complex issues such as suicide is to have a diversity of instruments and techniques that adjust to the characteristics of the population and that allow to understand the phenomena from the social constructs and not only theoretical. The constant study of suicide is a pressing need, the loss of a life from emotional difficulties that can be solved through psychiatry and psychological methods requires governments and professionals to pay attention and work with the risk population.

Keywords: adolescents, psychological construct, semantic networks, suicide

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Authors: Mohsen Maraoui

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In the aim of natural language processing applications improvement, such as information retrieval, machine translation, lexical disambiguation, we focus on statistical approach to semantic indexing for multilingual text documents based on conceptual network formalism. We propose to use this formalism as an indexing language to represent the descriptive concepts and their weighting. These concepts represent the content of the document. Our contribution is based on two steps. In the first step, we propose the extraction of index terms using the multilingual lexical resource Euro WordNet (EWN). In the second step, we pass from the representation of index terms to the representation of index concepts through conceptual network formalism. This network is generated using the EWN resource and pass by a classification step based on association rules model (in attempt to discover the non-taxonomic relations or contextual relations between the concepts of a document). These relations are latent relations buried in the text and carried by the semantic context of the co-occurrence of concepts in the document. Our proposed indexing approach can be applied to text documents in various languages because it is based on a linguistic method adapted to the language through a multilingual thesaurus. Next, we apply the same statistical process regardless of the language in order to extract the significant concepts and their associated weights. We prove that the proposed indexing approach provides encouraging results.

Keywords: concept extraction, conceptual network formalism, fuzzy association rules, multilingual thesaurus, semantic indexing

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: Robert Krause

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Primary progressive aphasia (PPA) is a neurodegenerative disease similar to frontotemporal and semantic dementia, while having a different clinical image and anatomic pathology topography. Nonetheless, they are often included under an umbrella term: frontotemporal lobar degeneration (FTLD). In the study, examples of diagnosing PPA are presented through the multidisciplinary lens of specialists from different fields (neurologists, psychiatrists, clinical speech therapists, clinical neuropsychologists and others) using a variety of diagnostic tools such as MR, PET/CT, genetic screening and neuropsychological and logopedic methods. Thanks to that, specialists can get a better and clearer understanding of PPA diagnosis. The study summarizes the concrete procedures and results of different specialists while diagnosing PPA in a patient of younger middle age and illustrates the importance of multidisciplinary approach to differential diagnosis of PPA.

Keywords: primary progressive aphasia, etiology, diagnosis, younger middle age

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Authors: Akrem Sellami, Imed Riadh Farah

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Hyperspectral imagery (HSI) typically provides a wealth of information captured in a wide range of the electromagnetic spectrum for each pixel in the image. Hence, a pixel in HSI is a high-dimensional vector of intensities with a large spectral range and a high spectral resolution. Therefore, the semantic interpretation is a challenging task of HSI analysis. We focused in this paper on object classification as HSI semantic interpretation. However, HSI classification still faces some issues, among which are the following: The spatial variability of spectral signatures, the high number of spectral bands, and the high cost of true sample labeling. Therefore, the high number of spectral bands and the low number of training samples pose the problem of the curse of dimensionality. In order to resolve this problem, we propose to introduce the process of dimensionality reduction trying to improve the classification of HSI. The presented approach is a semi-supervised band selection method based on spatial hypergraph embedding model to represent higher order relationships with different weights of the spatial neighbors corresponding to the centroid of pixel. This semi-supervised band selection has been developed to select useful bands for object classification. The presented approach is evaluated on AVIRIS and ROSIS HSIs and compared to other dimensionality reduction methods. The experimental results demonstrate the efficacy of our approach compared to many existing dimensionality reduction methods for HSI classification.

Keywords: dimensionality reduction, hyperspectral image, semantic interpretation, spatial hypergraph

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Authors: Munaf Rashid

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For content-based human action retrieval systems, search accuracy is often inferior because of the following two reasons 1) global information pertaining to videos is totally ignored, only low level motion descriptors are considered as a significant feature to match the similarity between query and database videos, and 2) the semantic gap between the high level user concept and low level visual features. Hence, in this paper, we propose a method that will address these two issues and in doing so, this paper contributes in two ways. Firstly, we introduce a method that uses both global and local information in one framework for an action retrieval task. Secondly, to minimize the semantic gap, a user concept is involved by incorporating features weight updating (FWU) Relevance Feedback (RF) approach. We use statistical characteristics to dynamically update weights of the feature descriptors so that after every RF iteration feature space is modified accordingly. For testing and validation purpose two human action recognition datasets have been utilized, namely Weizmann and UCF. Results show that even with a number of visual challenges the proposed approach performs well.

Keywords: relevance feedback (RF), action retrieval, semantic gap, feature descriptor, codebook

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Authors: Qinghua Zhang, Yanhe Zhu, Xiang Zhao, Yeqin Yang, Hongwei Jing, Guoan Zhang, Jie Zhao

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This paper presents a wearable reconfigurable supernumerary robotic limb with differential actuated joints, which is lightweight, compact and comfortable for the wearers. Compared to the existing supernumerary robotic limbs which mostly adopted series structure with large movement space but poor carrying capacity, a prototype with the series-parallel configuration to better adapt to different task requirements has been developed in this design. To achieve a compact structure, two kinds of cable-driven mechanical structures based on guide pulleys and differential actuated joints were designed. Moreover, two different tension devices were also designed to ensure the reliability and accuracy of the cable-driven transmission. The proposed device also employed self-designed bearings which greatly simplified the structure and reduced the cost.

Keywords: cable-driven, differential actuated joints, reconfigurable, supernumerary robotic limb

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Daniil Karzanov

Abstract:

This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly.

Keywords: stock market, earnings reports, financial time series, structural breaks, stochastic differential equations

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Davood Domiri Danji

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In this conference, our aims are accuracy, capabilities and power at solving of the complicated non-linear partial differential. Our purpose is to enhance the ability to solve the mentioned nonlinear differential equations at basic science and engineering field and similar issues with a simple and innovative approach. As we know most of engineering system behavior in practical are nonlinear process (especially basic science and engineering field, etc.) and analytical solving (no numeric) these problems are difficult, complex, and sometimes impossible like (Fluids and Gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure an innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical method (Runge-Kutta 4th). Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear partial differential equations, with help of that there is no difficulty for solving all nonlinear differential equations. Advantages and ability of this method (AGM) as follow: (a) Non-linear Differential equations (ODE, PDE) are directly solvable by this method. (b) In this method (AGM), most of the time, without any dimensionless procedure, we can solve equation(s) by any boundary or initial condition number. (c) AGM method always is convergent in boundary or initial condition. (d) Parameters of exponential, Trigonometric and Logarithmic of the existent in the non-linear differential equation with AGM method no needs Taylor expand which are caused high solve precision. (e) AGM method is very flexible in the coding system, and can solve easily varieties of the non-linear differential equation at high acceptable accuracy. (f) One of the important advantages of this method is analytical solving with high accuracy such as partial differential equation in vibration in solids, waves in water and gas, with minimum initial and boundary condition capable to solve problem. (g) It is very important to present a general and simple approach for solving most problems of the differential equations with high non-linearity in engineering sciences especially at civil engineering, and compare output with numerical method (Runge-Kutta 4th) and Exact solutions.

Keywords: new approach, AGM, sets of coupled nonlinear differential equation, exact solutions, numerical

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

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Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

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Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

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The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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