Numerical algorithm for nonlinear fractional equations with nonlocal boundary conditions based on a modified minimum residual method-Reference-Cited by-同舟云学术

Numerical algorithm for nonlinear fractional equations with nonlocal boundary conditions based on a modified minimum residual method

Published:2022-01-24 Issue:0 Volume:0 Page:
ISSN:2191-0294
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Jiang Wei¹^ORCID,Yue Zihan¹,Chen Zhong¹,Wu Fei¹

Affiliation:

1. Department of Mathematics , Harbin Institute of Technology , Weihai , Shangdong , 264209 , P.R. China

Abstract

Abstract In this paper, we will solve a nonlinear time-fractional equation with nonlocal boundary conditions. First, we construct a set of suitable base according to the correlation theory of reproducing kernel space and the nonlocal boundary conditions. Then we introduce F-derivative and Newton iterative to linearize the nonlinear terms of the equation. The appropriate initial iteration value is constructed by boundary conditions. Finally, we use the ɛ-approximate solution theory to solve the system of linear equations and give the corresponding theoretical derivation. In conclusion, several numerical examples illustrate the feasibility and effectiveness of the method.

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-2021-0230/pdf

Reference23 articles.

1. S. Patnaik, S. Sidhardh, and F. Semperlotti, “Nonlinear thermoelastic fractional-order model of nonlocal plates: application to postbuckling and bending response,” Thin-Walled Struct., vol. 164, p. 107809, 2021. https://doi.org/10.1016/j.tws.2021.107809.

2. O. Zaid and M. Shaher, “The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics,” Comput. Math. Appl., vol. 58, pp. 2199–2208, 2009. https://doi.org/10.1016/j.camwa.2009.03.009.

3. C. Wu and W. Rui, “Method of separation variables combined with homogenous balanced principle for searching exact solutions of nonlinear time-fractional biological population model,” Commun. Nonlinear Sci. Numer. Simulat., vol. 63, pp. 88–100, 2018. https://doi.org/10.1016/j.cnsns.2018.03.009.

4. B. P. Moghaddam and J. A. T. Machado, “A stable three-level explicit spline finite difference scheme for a class of nonlinear time variable order fractional partial differential equations,” Comput. Math. Appl., vol. 73, no. 6, pp. 1262–1269, 2017. https://doi.org/10.1016/j.camwa.2016.07.010.

5. J. Duan, T. Chaolu, R. Rach, and L. Lu, “The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations,” Comput. Math. Appl., vol. 66, no. 5, pp. 728–736, 2013. https://doi.org/10.1016/j.camwa.2013.01.019.