Search results for: differential metabolites

Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh

Abstract:

The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.

Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method

Procedia PDF Downloads 320

Authors: Weihua Ruan, Kuan-Chou Chen

Abstract:

This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Hamilton-Jacobi-Bellman equations, infinite-horizon differential games, continuous and discrete state variables, political-economy models

Procedia PDF Downloads 345

Authors: Christian A. Romero, Tanja Grkovic, John. R. J. French, D. İpek Kurtböke, Ronald J. Quinn

Abstract:

A high-throughput and automated 1H NMR metabolic fingerprinting dereplication approach was used to accelerate the discovery of unknown bioactive secondary metabolites. The applied dereplication strategy accelerated the discovery of natural products, provided rapid and competent identification and quantification of the known secondary metabolites and avoided time-consuming isolation procedures. The effectiveness of the technique was demonstrated by the isolation and elucidation of arglecins B (1), C (2) and actinofuranosin A (3) from a termite-gut associated Streptomyces sp. (USC 597) grown under solid state fermentation. The structures of these compounds were elucidated by extensive interpretation of 1H, 13C and 2D NMR spectroscopic data. These represent the first report of arglecin analogs isolated from a termite gut-associated Streptomyces species.

Keywords: actinomycetes, actinofuranosin, antibiotics, arglecins, NMR spectroscopy

Procedia PDF Downloads 27

Authors: Martin K. Steiger, Lukas Heisler, Hans-Georg Brachtendorf

Abstract:

Deep neural networks and their variants form the backbone of many AI applications. Based on the so-called residual networks, a continuous formulation of such models as ordinary differential equations (ODEs) has proven advantageous since different techniques may be applied that significantly increase the learning speed and enable controlled trade-offs with the resulting error at the same time. For the evaluation of such models, high-performance numerical differential equation solvers are used, which also provide the gradients required for training. However, whether classical gradient-based methods are even applicable or which one yields the best results has not been discussed yet. This paper aims to redeem this situation by providing empirical results for different applications.

Keywords: deep neural networks, gradient-based learning, image processing, ordinary differential equation networks

Procedia PDF Downloads 130

Authors: Chao-Qing Dai

Abstract:

In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

Procedia PDF Downloads 633

Authors: Susan Hall, Gary D. Grant, Catherine McDermott, Devinder Arora

Abstract:

Introduction /Aim: The kynurenine pathway is thought to play an important role in the pathophysiology of numerous neurodegenerative diseases including depression, Alzheimer’s disease, and Parkinson’s disease. Numerous neuroactive compounds, including the neurotoxic 3-hydroxyanthranilic acid, 3-hydroxykynurenine and quinolinic acid and the neuroprotective kynurenic acid and picolinic acid, are produced through the metabolism of kynurenine and are thought to be the causative agents responsible for neurodegeneration. The toxicity of 3-hydroxykynurenine, 3-hydroxyanthranilic acid and quinolinic acid has been widely evaluated and demonstrated in primary cell cultures but to date only 3-hydroxykynurenine and 3-hydroxyanthranilic acid have been shown to cause toxicity in immortal tumour cells. The aim of this study was to evaluate the toxicity of kynurenine metabolites, both individually and in combination, on SH-SY5Y neuroblastoma cells after 24 and 72 h exposure in order to explore a cost-effective model to study their neurotoxic effects and potential protective agents. Methods: SH-SY5Y neuroblastoma cells were exposed to various concentrations of the neuroactive kynurenine metabolites, both individually and in combination, for 24 and 72 h, and viability was subsequently evaluated using the Resazurin (Alamar blue) proliferation assay. Furthermore, the effects of these compounds, alone and in combination, on specific death pathways including apoptosis, necrosis and free radical production was evaluated using various assays. Results: Consistent with literature, toxicity was shown with short-term 24-hour treatments at 1000 μM concentrations for both 3-hydroxykynurenine and 3-hydroxyanthranilic acid. Combinations of kynurenine metabolites showed modest toxicity towards SH-SY5Y neuroblastoma cells in a concentration-dependent manner. Specific cell death pathways, including apoptosis, necrosis and free radical production were shown to be increased after both 24 and 72 h exposure of SH-SY5Y neuroblastoma cells to 3-hydroxykynurenine and 3-hydroxyanthranilic acid and various combinations of neurotoxic kynurenine metabolites. Conclusion: It is well documented that neurotoxic kynurenine metabolites show toxicity towards primary human neurons in the nanomolar to low micromolar concentration range. Results show that the concentrations required to show significant cell death are in the range of 1000 µM for 3-hydroxykynurenine and 3-hydroxyanthranilic acid and toxicity of quinolinic acid towards SH-SY5Y was unable to be shown. This differs significantly from toxicities observed in primary human neurons. Combinations of the neurotoxic metabolites were shown to have modest toxicity towards these cells with increased toxicity and activation of cell death pathways observed after 72 h exposure. This study suggests that the 24 h model is unsuitable for use in neurotoxicity studies, however, the 72 h model better represents the observations of the studies using primary human neurons and may provide some benefit in providing a cost-effective model to assess possible protective agents against kynurenine metabolite toxicities.

Keywords: kynurenine metabolites, neurotoxicity, quinolinic acid, SH-SY5Y neuroblastoma

Procedia PDF Downloads 396

Authors: Nishtha, Richa, Anju Rao

Abstract:

Plants are the source of herbal medicine and medicinal value of the plants lies in the bioactive phytochemical constituents that produce definite physiological effects on human body. Angiospermic families are known to produce such phytochemical constituents which are termed as secondary plant metabolites. These metabolites include alkaloids, saponins, phenolic compounds, flavonoids, tannins, terpenoids and so on. Solanaceae is one of the important families of Angiosperms known for medicinally important alkaloids such as hyoscyamine, scopolamine, solanine, nicotine, capsaicin etc. Medicinally important species of this family mostly belong to the genera of Datura,Atropa,Solanum,Withania and Nicotiana.Six species such as Datura metel, Solanum torvum, Physalis minima, Cestrum nocturnum, Cestrum diurnum and Nicotiana plumbaginifolia have been collected from different localities of Chandigarh and adjoining areas.Field and anatomical studies helped to identify the plants and their parts used for the study of secondary plant metabolites. Preliminary phytochemcial studies have been done on various parts of plants such as roots, stem and leaves by making aqueous and alcoholic extracts from their powdered forms which showed the presence of alkaloids in almost all the species followed by steroids, flavonoids, terpenoids, tannins etc. HPLC profiles of leaves of Datura metel showed the presence of active compounds such as scopalamine and hyoscyamine and Solanum torvum showed the presence of solanine and solasodine. These alkaloids are important source of drug based medicine used in pharmacognosy. The respective compounds help in treating vomiting, nausea, respiratory disorders, dizziness, asthma and many heart problems.

Keywords: alkaloids, flavanoids, phytochemical constituents, pharmacognosy, secondary metabolites

Procedia PDF Downloads 416

Authors: Mary Chriselda A

Abstract:

This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

Procedia PDF Downloads 174

Authors: Malika Elkyal

Abstract:

We consider an iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm does not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Accordingly, we note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, differential algebraic equations

Procedia PDF Downloads 525

Authors: Fadila Mohamed Mahmoud., Derkaoui I., Krimi Z.

Abstract:

Date palm is a plant which presents a very good adaptation to the difficult conditions of the environment in particular to the drought and saline stress even at high temperatures. This adaptation is related on the biology of the plant and to the presence of a microflora endophyte which live inside its tissues. Fifteen endophytics fungi isolated from date palm were tested in vitro in the presence of various NaCl concentrations to select halotolerantes isolates. These same endophytes were tested for their colonizing capacity by the description of the production of secondary metabolites more particularly the enzymes (pectinases, proteases, and phosphorylases), and the production of antibiotics and growth hormones. Significant difference was observed between the isolates with respect to the tests carried out.

Keywords: Date palm, Halotolerantes, endophyte, Secondary metabolites.

Procedia PDF Downloads 485

Authors: Jeisson Alejandro Triana, Maria Fernanda Quiceno Vallejo, Patricia del Portillo, Juan Manuel Anzola

Abstract:

Most of the known antimicrobials so far discovered are secondary metabolites. The potential for new natural products of this category increases as new microbial genomes and metagenomes are being sequenced. Despite the advances, there is no systematic way to interrogate metagenomic clones for their potential to contain clusters of genes related to these pathways. Here we analyzed 52 biosynthetic pathways from the AntiSMASH database at the protein domain level in order to identify domains of high specificity and sensitivity with respect to specific biosynthetic pathways. These domains turned out to have various degrees of divergence at the DNA level. We propose PCR assays targetting such domains in-silico and corroborated one by Sanger sequencing.

Keywords: bioinformatic, anti smash, antibiotics, secondary metabolites, natural products, protein domains

Procedia PDF Downloads 144

Authors: T. Vamsee Kiran, A. Gopi

Abstract:

The undesired torque and flux ripple may occur in conventional direct torque control (DTC) induction motor drive. DTC can improve the system performance at low speeds by continuously tuning the regulator by adjusting the Kp, Ki values. In this differential evolution (DE) is proposed to adjust the parameters (Kp, Ki) of the speed controller in order to minimize torque ripple, flux ripple, and stator current distortion.The DE based PI controller has resulted is maintaining a constant speed of the motor irrespective of the load torque fluctuations.

Keywords: differential evolution, direct torque control, PI controller

Procedia PDF Downloads 398

Authors: Jiya Mohammed, Ibrahim Ismail Giwa

Abstract:

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

Procedia PDF Downloads 439

Authors: Maryam Mosleh, Mahmood Otadi

Abstract:

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

Procedia PDF Downloads 512

Authors: Elene Zhuravliova, Tamar Barbakadze, Irina Kalandadze, Elnari Zaalishvili, Lali Shanshiashvili, David Mikeladze

Abstract:

Background: Multiple sclerosis (MS) is an inflammatory, neurodegenerative disease, which is accompanied by demyelination and autoimmune response to myelin proteins. Among post-translational modifications, which mediate the modulation of inflammatory pathways during MS, methylation is the main one. The methylation of DNA, also amino acids lysine and arginine, occurs in the cell. It was found that decreased trans-methylation is associated with neuroinflammatory diseases. Therefore, abnormal regulation of the methyl cycle could induce demyelination through the action on PAD (peptidyl-arginine-deiminase) gene promoter. PAD takes part in protein citrullination and targets myelin basic protein (MBP), which is affected during demyelination. To determine whether MBP charge isomers are changing the methyl cycle, we have estimated the concentrations of methyl cycle metabolites in MBP-activated primary astrocytes and oligodendrocytes. For this purpose, the action of the citrullinated MBP- C8 and the most cationic MBP-C1 isomers on the primary cells were investigated. Methods: Primary oligodendrocyte and astrocyte cell cultures were prepared from whole brains of 2-day-old Wistar rats. The methyl cycle metabolites, including homocysteine, S-adenosylmethionine (SAM), and S-adenosylhomocysteine (SAH), were estimated by HPLC analysis using fluorescence detection and prior derivatization. Results: We found that the action of MBP-C8 and MBP-C1 induces a decrease in the concentration of both methyl cycle metabolites, S-adenosylmethionine (SAM) and S-adenosylhomocysteine (SAH), in astrocytes compared to the control cells. As for oligodendrocytes, the concentration of SAM was increased by the addition of MBP-C1, while MBP-C8 has no significant effect. As for SAH, its concentration was increased compared to the control cells by the action of both MBP-C1 and MBP-C8. A significant increase in homocysteine concentration was observed by the action of the MBP-C8 isomer in both oligodendrocytes and astrocytes. Conclusion: These data suggest that MBP charge isomers change the concentration of methyl cycle metabolites. MBP-C8 citrullinated isomer causes elevation of homocysteine in astrocytes and oligodendrocytes, which may be the reason for decreased astrocyte proliferation and increased oligodendrocyte cell death which takes place in neurodegenerative processes. Elevated homocysteine levels and subsequent abnormal regulation of methyl cycles in oligodendrocytes possibly change the methylation of DNA that activates PAD gene promoter and induces the synthesis of PAD, which in turn provokes the process of citrullination, which is the accompanying process of demyelination. Acknowledgment: This research was supported by the SRNSF Georgia RF17_534 grant.

Keywords: myelin basic protein, astrocytes, methyl cycle metabolites, homocysteine, oligodendrocytes

Procedia PDF Downloads 119

Authors: James Sinclair, Katy Soapi, Brad Carte

Abstract:

The marine environment has continuously demonstrated to be a rich source of secondary metabolites and bioactive compounds that can address the many pharmaceutical problems facing mankind. The emergence of multidrug resistant pathogens has caused scientists to explore contemporary ways of combating these super bugs. A red-pigmented bacterial strain isolated from a marine alga collected in Fiji was identified to be Pseudoalteromonas rubra from 16s rRNA sequencing. This bacterial strain was cultured using a yeast-peptone media and incubated for five days. The ethyl acetate extract of this bacterium was subjected to chromatographic separation techniques such as vacuum liquid chromatography, flash chromatography, size exclusion chromatography and high-pressure liquid chromatography to yield the pure compound and a number of semi-pure fractions. The crude extract and subsequent purified fractions were analyzed by ultraviolet/visible spectroscopy and mass spectroscopy and was found to contain the compounds ivermectin, stenothricin, cyclo-L-pro-L-val, prodigiosin, mycophenolic acid, phenazine-1-carboxylic acid, eplerenone, staurosporine and pseudoalteromone A. The structure of the pure compound, pseudoalteromone A, was elucidated using NMR 1H, 13C, 1H-1H COSY, HSQC and HMBC spectroscopic data.

Keywords: Pseudoalteromonas rubra, Pseudoalteromone A, secondary metabolites, structure elucidation

Procedia PDF Downloads 177

Authors: Chien-Liang Chao, Yun-Sheng Lin

Abstract:

Secondary metabolites are applied in the human life of the Chinese herbal medicine. Many drugs are originally extracted from natural products with combination of pharmaceutical and chemical studies. Crude extract of the leaves from Zamia furfureace L. has been shown to exhibit anticancer activities. The first chemical investigation of this plant was carried out by our group. In this study, four known compounds were isolated from Zamia furfureace L. with three lignins (Sesamin (1), Wodeshiol (2) and Paulownin (3)), and one dipeptide (Aurantiamide acetate (4)). The structures of these compounds were analyzed through the 1D-NMR(1H-NMR,13C-NMR)、2D-NMR(COSY、HMQC、HMBC、NOESY) spectroscopic analysis, and by comparison of variety of physical data (IR, mass spectrometry, ultraviolet, optical rotation). Among them, Aurantiamide acetate (4) exhibited weak cytotoxic activity against human gastric cancer cells.

Keywords: Zamia furfureace L., AGS, sesamin, Aurantiamide acetate, secondary metabolites

Procedia PDF Downloads 456

Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

Abstract:

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

Procedia PDF Downloads 194

Authors: Somveer Singh, Vineet Kumar Singh

Abstract:

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

Procedia PDF Downloads 300

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

Abstract:

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

Procedia PDF Downloads 437

Authors: Ramdas Sonawane, Mahaveer Gadiya

Abstract:

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

Procedia PDF Downloads 408

Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

Abstract:

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

Procedia PDF Downloads 325

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

Abstract:

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

Procedia PDF Downloads 182

Authors: Rekha Vijayvergia

Abstract:

Around seven percent of tribal population of India lives in Rajasthan. Rajasthan has rich cultural diversity and biodiversity. Ethno-botany can be defined as the total natural and traditional relationship and the interactions between man and his surrounding plant wealth from times immemorial, due to sheer, necessity, intuition, observation, and experimentation. Medicinal plants are valuable and are used for the production of various drugs. These plants produce a high diversity of natural products or secondary metabolites like Mahanimbicine, Andrographine, murrayaline, lupeol, and limonin etc. with a prominent function in the protection against diseases like diabetes, kidney stones, osteoporosis, tumours, opthalmia, leucorrhoea, bronchial asthma, diarrhea, cancer, etc. The present report gives an account of traditional medicinal uses of common medicinal plants of Rajasthan. A total of 18 plant species belonging to 13 families are reported, that are being used for various purposes.

Keywords: ethno botany, Rajasthan, secondary metabolites, traditional medicines

Procedia PDF Downloads 464

Authors: Haniye Dehestani, Yadollah Ordokhani

Abstract:

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

Procedia PDF Downloads 140

Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

Abstract:

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

Procedia PDF Downloads 356

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

Procedia PDF Downloads 164

Authors: Somveer Singh, Vineet Kumar Singh

Abstract:

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

Procedia PDF Downloads 405

Authors: A. Guezane-Lakoud, S. Bensebaa

Abstract:

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

Procedia PDF Downloads 382

Authors: Youssef Abdelli, Rachid Nasri

Abstract:

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

Procedia PDF Downloads 427