Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order-Reference-Cited by-同舟云学术

Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

Published:2018-06-01 Issue:1 Volume:3 Page:255-264
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Talay Akyildiz F.¹,Vajravelu K.²

Affiliation:

1. Department of Mathematics and Statistics , Faculty of Science , Al-Imam University , Riyadh , Saudi Arabia

2. Department of Mathematics , University of Central Florida , Orlando , Florida 32816 , USA

Abstract

Abstract In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization. In addition, we use this novel method to solve the well-known semi-linear Poisson-Boltzmann (PB) model equation and obtain solutions with higher-order accuracy. Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement. Furthermore, our new technique is also applicable for three-dimensional problems.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Link

https://www.sciendo.com/pdf/10.21042/AMNS.2018.1.00019

Reference15 articles.

1. Z. F. Tian and Y. B. Ge,1.(2007), A fourth-order compact ADI method for solving two-dimensional unsteady convection-diffusion problems, J. Comput. Appl. Math. 198, 268-286. 10.1016/j.cam.2005.12.005

2. A. Mohebbi and M. Dehghan,2.(2010), High-order compact solution of the one-dimensional heat and advection diffusion equations. Appl. Math. Model. 34, 3071-3084. 10.1016/j.apm.2010.01.01310.1016/j.apm.2010.01.013

3. A. Lasis and E. Süli,3.(2007), hp-Version Discontinuous Galerkin Finite Element Methods for Semilinear Parabolic Problems, SIAM J. Numer. Anal.45(4), 1544-1569. 10.1137/05064212510.1137/050642125

4. C. Chen and W. Liu,4.(2010), Two-grid finite volume element methods for semilinear parabolic problems, Applied Numerical Mathematics, January-February, Volume 60, Issues 1-2, Pages 10-18. 10.1016/j.apnum.2009.08.00410.1016/j.apnum.2009.08.004

5. W. Liu, J. Sun and B. Wu,5.(2016), Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations, Numer Algor. 71, 437-455. 10.1007/s110710.1007/s11075-015-0002-x

Cited by 14 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Explicit Chebyshev–Galerkin scheme for the time-fractional diffusion equation;International Journal of Modern Physics C;2023-06-30

2. Imposed magnetic field impact on vortex generation in the laminar nanofluid flow: A computational approach;International Communications in Heat and Mass Transfer;2022-12

3. Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises;Applied Mathematics and Nonlinear Sciences;2022-07-15

4. CCR model-based evaluation on the effectiveness and maturity of technological innovation;Journal of Industrial & Management Optimization;2022

5. Establishment of the model on the expression and guidance of contemporary college students’ demands in the cyberspace environment;Complex & Intelligent Systems;2021-11-08