Search results for: merit order

Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Mahdi Shamsi, Tohid Yousefi Rezaii, Siavash Eftekharifar

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Compressed sensing (CS) is a new powerful mathematical theory concentrating on sparse signals which is widely used in signal processing. The main idea is to sense sparse signals by far fewer measurements than the Nyquist sampling rate, but the reconstruction process becomes nonlinear and more complicated. Common dilemma in sparse signal recovery in CS is the lack of knowledge about sparsity order of the signal, which can be viewed as model order selection procedure. In this paper, we address the problem of sparsity order estimation in sparse signal recovery. This is of main interest in situations where the signal sparsity is unknown or the signal to be recovered is approximately sparse. It is shown that the proposed method also leads to some kind of signal denoising, where the observations are contaminated with noise. Finally, the performance of the proposed approach is evaluated in different scenarios and compared to an existing method, which shows the effectiveness of the proposed method in terms of order selection as well as denoising.

Keywords: compressed sensing, data denoising, model order selection, sparse representation

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Atje Setiawan Abdullah, Budi Nurani Ruchjana, I. Gede Nyoman Mindra Jaya, Eddy Hermawan

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Ethnoscience is used to see the culture with a scientific perspective, which may help to understand how people develop various forms of knowledge and belief, initially focusing on the ecology and history of the contributions that have been there. One of the areas studied in ethnoscience is etno-informatics, is the application of informatics in the culture. In this study the science of informatics used is data mining, a process to automatically extract knowledge from large databases, to obtain interesting patterns in order to obtain a knowledge. While the application of culture described by naming database village on the island of Java were obtained from Geographic Indonesia Information Agency (BIG), 2014. The purpose of this study is; first, to classify the naming of the village on the island of Java based on the structure of the word naming the village, including the prefix of the word, syllable contained, and complete word. Second to classify the meaning of naming the village based on specific categories, as well as its role in the community behavioral characteristics. Third, how to visualize the naming of the village to a map location, to see the similarity of naming villages in each province. In this research we have developed two theorems, i.e theorems area as a result of research studies have collected intersection naming villages in each province on the island of Java, and the composition of the wedge theorem sets the provinces in Java is used to view the peculiarities of a location study. The methodology in this study base on the method of Knowledge Discovery in Database (KDD) on data mining, the process includes preprocessing, data mining and post processing. The results showed that the Java community prioritizes merit in running his life, always working hard to achieve a more prosperous life, and love as well as water and environmental sustainment. Naming villages in each location adjacent province has a high degree of similarity, and influence each other. Cultural similarities in the province of Central Java, East Java and West Java-Banten have a high similarity, whereas in Jakarta-Yogyakarta has a low similarity. This research resulted in the cultural character of communities within the meaning of the naming of the village on the island of Java, this character is expected to serve as a guide in the behavior of people's daily life on the island of Java.

Keywords: ethnoscience, ethno-informatics, data mining, clustering, Java island culture

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Sandeep Singh

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In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: Gubhinder Kundhi, Paul Rilstone

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Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: edgeworth expansions, higher order asymptotics, saddlepoint expansions, weak instruments

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Authors: Ying Yi Wu

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The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Ali Ait Si Mhamed, Rita Kasa, Hans Vossensteyn

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Kazakhstan is the eight largest country on the globe, in terms of the territory, it is rich in natural resources and is developing dynamically. Kazakhstan strives to become one of the top 30 global economies by 2050. This goal preconditions intensive reforms in all sectors of economy, including higher education. This paper focuses on the higher education funding reforms that take place in Kazakhstan and their alignment with the strategic goals of national development. Currently, the government funds higher education costs for only a limited number of students while the majority of students pay full cost covering tuition fees. Only students with high examination scores at the end of the secondary education are eligible to be admitted to publically funded study places in higher education. While this merit-based higher education funding model is overall well-received in the country, there is also a discourse calling to change the existing approach of higher education funding. This paper draws on interviews with national policy makers and leadership at institutions of higher education in Kazakhstan collected during 2016. It seeks to answer a question about how well the current higher education funding mechanism is aligned with the strategic development goals in higher education. The paper discusses how stakeholders see the fit between the current higher education funding mechanism and the ability of higher education institutions to achieve the aims of national strategic development.

Keywords: higher education reform, higher education funding, higher education policy, Kazakhstan

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Authors: Asiye Aydilek, Harun Aydilek

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We investigate the costs of various suboptimal allocations in housing, consumption, bond and stock holdings of a retiree in a setting with recursive utility, considering the extensive empirical evidence that investors make suboptimal decisions in different ways. We find that suboptimal stock holdings impose only modest costs on the retiree. This may have a merit in explaining the limited stock investment in the data. The cost of suboptimal bond holdings is higher than that of stocks, but still small. This may partially explain why many more people hold bonds compared to stocks. We find that positive deviations from the optimal level are less costly relative to the negative ones in suboptimal housing allocations. This may help us to clarify why the elderly are over consuming housing, as seen in the housing data. The cost of suboptimal consumption is quite high and the highest of all. Our paper suggests that, in terms of welfare, the decisions of how much of liquid wealth to use for consumption and for saving are more important than the decision about the composition of liquid savings. Suboptimal stock holdings are twice more costly in power utility and suboptimal bond holdings are twenty times more costly in recursive utility. Recursive utility is superior to power utility in terms of rationalizing many people's preference for bonds instead of stocks in investment.

Keywords: housing, recursive utility, retirement, suboptimal decisions, welfare cost

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Authors: Moh'd Alodat

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In this paper, we discuss the power function distribution and derive the maximum likelihood estimator of its parameter as well as the reliability parameter. We derive the large sample properties of the estimators based on the selective order statistic scheme. We conduct simulation studies to investigate the significance of the selective order statistic scheme in our setup and to compare the efficiency of the new proposed estimators.

Keywords: fisher information, maximum likelihood estimator, power function distribution, ranked set sampling, selective order statistics sampling

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Salisu Ibrahim

Abstract:

The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, analog control

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Authors: Salisu Ibrahim

Abstract:

The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, and analog control

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Authors: Huei Chu Weng

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This paper presents a study on the effect of second-order slip on forced convection through a long isoflux heated or cooled planar microchannel. The fully developed solutions of flow and thermal fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and local heat flux boundary conditions. Results reveal that when the average flow velocity increases or the wall heat flux amount decreases, the role of thermal creep becomes more insignificant, while the effect of second-order slip becomes larger. The second-order term in the Deissler slip boundary condition is found to contribute a positive velocity slip and then to lead to a lower pressure drop as well as a lower temperature rise for the heated-wall case or to a higher temperature rise for the cooled-wall case. These findings are contrary to predictions made by the Karniadakis slip model.

Keywords: microfluidics, forced convection, thermal creep, second-order boundary conditions

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Authors: Budsarin Padwang, Darunee Jongudomkarn, Thawan Nieamsup, Autchareeya Patumwan, Rutja Phuphaibul

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In Northern Thailand, a pilot study by the qualitative data, on caring for family members with chronic illness/bedridden based on in-depth interviews of the 12 elderly caregivers in family was carried out during November to December 2017. There are four families that living with three generations in the family. This report is part of a larger study of 'The intergenerational contract of the family in long-term care for older members' to understand the situation and context related to the research questions. Content analysis was obtained and the results revealed as followings. 1) No choice and no freedom: most caregivers were asked by their family members to do the care giving roles because of various appropriate reasons and they could not refuse and felt like having no freedom. 2) ‘Katanyu’ to the parents: The Thai ideology of making merit by taking care of parents was beliefs to do the best in their caregiver roles. 3) The family commitments: The issues of family caring and relationships were the key value of keeping family members to take care of older members with chronic illness/bedridden. The preliminary findings can be beneficial for other regions and will lead to in-depth explore to answer the research questions of the larger study in the future.

Keywords: intergenerational contract, long term care, older members, generational family

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Abdulkabir Abdullahi

Abstract:

Nigeria has not yet welcomed phonics into its primary schools. In government-owned primary schools teachers are functionally ignorant of the stories of the reading wars amongst international scholars. There are few or no Nigerian-authored phonics textbooks, and there has been no government-owned phonics curriculum either. There are few or no academic journal articles on phonics in the country and there is, in fact, a certain danger of confusion between phonics and phonetics among Nigerian publishers, authors, writers and academics as if Nigerian teachers of English and the educational policy makers of the country were unaware of reading failures/problems amongst Nigerian children, or had never heard of phonics or read of the stories of the reading wars or the annual phonics test in the United Kingdom, the United States of America and other parts of the world. It is on this note that this article reviews and examines, in the style of a qualitative inquiry, the body of arguments on phonics, and explores the effectiveness of phonics teaching, particularly, in a second-language learning contexts. While the merit of the paper is, perhaps, situated in its supreme effort to draw global attention to reading failures/problems in Nigeria and the ways the situation may affect English language learning, international academic relations and the educational future of the country, it leaves any quantitative verification of its claims to interested quantitative researchers in the world.

Keywords: graphemes, phonics, reading, reading wars, reading theories, phonemic awareness

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Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane

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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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Authors: Brando Vagenende, Marie-Anne Guerry

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For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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Authors: Christopher Viens, Steve Krase

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Terms such as “riding a hard streak”, “formation push”, and “fighting formation” are commonly used in the directional drilling world to explain BHA behavior that causes unwanted trajectory change. Theories about downhole directional tendencies are commonly speculated from various personal experiences with little merit due to the lack of hard data to reveal the actual mechanisms behind the phenomenon, leaving interpretation of the root cause up to personal perception. Understanding and identifying in real time the lithological factors that influence the BHA to change or hold direction adds tremendous value in terms reducing sliding time and targeting zones for optimal ROP. Utilizing surface drilling parameters and employing downhole measurements of azimuthal gamma, continuous inclination, and bending moment, a direct measure of the rock related directional phenomenon have been captured and quantified. Furthermore, identifying continuous zones of like lithology with consistent bit to rock interaction has value from a reservoir characterization and completions standpoint. The paper will show specific examples of lithology related directional tendencies from the Spraberry and Wolfcamp in the Delaware Basin.

Keywords: Azimuthal gamma imaging, bending moment, continuous inclination, downhole dynamics measurements, high frequency data

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Authors: Fouzi Aboura

Abstract:

The fractional order proportional-integral-derivative (FOPID) controller or fractional order (PIλDµ) is a proportional-integral-derivative (PID) controller where integral order (λ) and derivative order (µ) are fractional, one of the important application of classical PID is the Automatic Voltage Regulator (AVR).The FOPID controller needs five parameters optimization while the design of conventional PID controller needs only three parameters to be optimized. In our paper we have proposed a comparison between algorithms Differential Evolution (DE) and Hybrid Genetic Algorithm Particle Swarm Optimization (HGAPSO) ,we have studied theirs characteristics and performance analysis to find an optimum parameters of the FOPID controller, a new objective function is also proposed to take into account the relation between the performance criteria’s.

Keywords: FOPID controller, fractional order, AVR system, objective function, optimization, GA, PSO, HGAPSO

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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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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Authors: Matthew C. Best

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Linear Multi-Input Multi-Output (MIMO) dynamic models can be identified, with no a priori knowledge of model structure or order, using a new Generalised Identifying Filter (GIF). Based on an Extended Kalman Filter, the new filter identifies the model iteratively, in a continuous modal canonical form, using only input and output time histories. The filter’s self-propagating state error covariance matrix allows easy determination of convergence and conditioning, and by progressively increasing model order, the best fitting reduced-order model can be identified. The method is shown to be resistant to noise and can easily be extended to identification of smoothly nonlinear systems.

Keywords: system identification, Kalman filter, linear model, MIMO, model order reduction

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Authors: A. M. Sagir

Abstract:

Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Bahareh Arghand

Abstract:

The establishment of rules and regulations for more effective energy-environment interactions are essential to achieving sustainable development. Sustainable development requires mechanisms that can promote compliance in energy-environment conventions. There are many binding agreements and non-binding instruments at regional and international levels on energy and the environment. These conventions try to decrease conflicts of interest between energy, environment and economic by legal principles and practical mechanisms. The major core of conventions is their implementations because the poor implementation and enforcement power affect their success. In this regard, the main goal of this study is proposing the effective implementation mechanisms. Energy service companies' (ESCOs) activities can improve energy efficiency and decrease the environmental degradations. Therefore, it can be proposed and assessed the merit mechanism of ESCO performance as a facilitator to implement energy-environment conventions. An assessment of ESCO performance, including its potentials, problems, and limitations, as a facilitator for effective implementation of the energy-environment convention, is included. This study is oriented towards effective development and application of laws and the function of ESCOs as appropriate economic instruments and facilitator for implementation of energy-environment conventions. The resulting system of close cooperation between the energy-environment conventions and ESCOs is geared toward advancing environmental protection and economic factors by the transfer of environmentally-sound technologies that meet sustainable development objectives.

Keywords: energy-environment conventions, energy service company, facilitator mechanism, sustainable development

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Aurore Cauquis, Philippe Heinrich, Mario Ricchiuto, Audrey Gailler

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In this talk, we look for an accurate time scheme to model the propagation of waves. Several numerical schemes have been developed to solve the extended weakly nonlinear weakly dispersive Boussinesq Equations. The temporal schemes used are two Lax-Wendroff schemes, second or third order accurate, two Runge-Kutta schemes of second and third order and a simplified third order accurate Lax-Wendroff scheme. Spatial derivatives are evaluated with fourth order accuracy. The numerical model is applied to two monodimensional benchmarks on a flat bottom. It is also applied to the simulation of the Algerian tsunami generated by a Mw=6 seism on the 18th March 2021. The tsunami propagation was highly dispersive and propagated across the Mediterranean Sea. We study here the effects of the order of temporal discretization on the accuracy of the results and on the time of computation.

Keywords: numerical analysis, tsunami propagation, water wave, boussinesq equations

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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