Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems-Reference-Cited by-同舟云学术

Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems

Published:2021-09-13 Issue:0 Volume:0 Page:
ISSN:2191-0294
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Singh Harendra¹

Affiliation:

1. Department of Mathematics , Post-Graduate College , Ghazipur 233001 , Uttar Pradesh , India

Abstract

Abstract This paper deals with a class of Bratu’s type, Troesch’s and nonlocal elliptic boundary value problems. Due to strong nonlinearity and presence of parameter δ, it is very difficult to solve these problems. Here we solve these classes of important equations using the Chebyshev spectral collocation method. We have provided the convergence of the proposed approximate method. The trueness of the method is shown by applying it to some illustrative examples. Results are compared with some known methods to highlight its neglectable error and high accuracy.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2020-0235/pdf

Reference49 articles.

1. V. Ananthaswamy and L. Rajendran, “Analytical solutions of some two-point non-linear elliptic boundary value problems,” Appl. Math., vol. 3, no. 9, p. 1044, 2012. https://doi.org/10.4236/am.2012.39154.

2. Y. Lin, J. A. Enszer, and M. A. Stadtherr, “Enclosing all solutions of two-point boundary value problems for ODEs,” Comput. Chem. Eng., vol. 32, no. 8, pp. 1714–1725, 2008. https://doi.org/10.1016/j.compchemeng.2007.08.013.

3. J. Newman and W. Tiedemann, “Porous-electrode theory with battery applications,” AIChE J., vol. 21, no. 1, pp. 25–41, 1975. https://doi.org/10.1002/aic.690210103.

4. H. Singh, F. A. Ghassabzadeh, E. Tohidi, and C. Cattani, “Legendre spectral method for the fractional Bratu problem,” Math. Methods Appl. Sci., vol. 43, no. 9, pp. 5941–5952, 2020. https://doi.org/10.1002/mma.6334.

5. H. Singh, A. K. Singh, R. K. Pandey, D. Kumar, and J. Singh, “An efficient computational approach for fractional Bratu’s equation arising in electrospinning process,” Math. Methods Appl. Sci., vol. 44, no. 13, pp. 10225–10238, 2021. https://doi.org/10.1002/mma.7401.

Cited by 19 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. The Analitical Solution of Linear and Non-Linear Differential- Algebraic Equations (DAEs) with Laplace-Padé Series Method;MANAS Journal of Engineering;2024-06-21

2. A numerical study on the nonlinear fractional Klein–Gordon equation;Journal of Umm Al-Qura University for Applied Sciences;2023-12-15

3. Stochastic resetting and linear reaction processes: A continuous time random walk approach;Communications in Nonlinear Science and Numerical Simulation;2023-11

4. An efficient wavelet‐based approximation method for solving nonlinear fractional‐time long wave equations: An operational matrix approach;Mathematical Methods in the Applied Sciences;2023-10-31

5. A Reliable Combination of Double Laplace Transform and Homotopy Analysis Method for Solving a Singular Nonlocal Problem with Bessel Operator;Axioms;2023-09-29