An efficient numerical technique for variable order time fractional nonlinear Klein-Gordon equation

被引：20

作者：

Hassani, H. ^{[1
]}

Machado, J. A. Tenreiro ^{[2
]}

Naraghirad, E. ^{[3
]}

机构：

[1] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[2] Polytech Porto, Inst Engn, Dept Elect Engn, R Dr Antonio Bernardino Almeida 431, P-4249015 Porto, Portugal

[3] Univ Yasuj, Dept Math, Yasuj, Iran

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 154卷

关键词：

Variable order time fractional nonlinear; Klein-Gordon equation; Variable order fractional derivatives; Generalized polynomials; Operational matrix; Lagrange multipliers; Control parameters; DIFFUSION-WAVE; LAGRANGE MULTIPLIERS; COLLOCATION METHOD; DIFFERENCE SCHEME; DIFFERENTIATION; CONVERGENCE; ALGORITHMS; UNIQUENESS; OPERATOR;

D O I：

10.1016/j.apnum.2020.04.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the variable order time fractional nonlinear Klein-Gordon equation (V-TFNKGE). An optimization method using the Caputo type definition and a set of basis functions, namely the generalized polynomials (GP), is proposed. The solution is expanded in terms of the GP with unknown free coefficients and control parameters. First, a new variable order time fractional operational matrix of the Caputo type for the GP is derived. Then, based on a operational matrix and the Lagrange multipliers, an optimization process achieves the approximate solution. Additionally, the convergence of the proposed method is analyzed and two numerical examples illustrate its good performance. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：260 / 272

页数：13

共 57 条

[51] A symplectic approximation with nonlinear stability and convergence analysis for efficiently solving semi-linear Klein-Gordon equations [J].