Nonlocal solution of a nonlinear partial differential equation and its equivalent of nonlinear integral equation

被引：0

作者：

Abdou M.A. ^{[1
,2
]}

Raad S.A. ^{[1
,2
]}

机构：

[1] Department of Mathematics, Faculty of Education Alexandria University, Alexandria

[2] Department of Mathematics, Faculty Applied Sciences, Umm Al-Qura University, Makkah

来源：

Abdou, M.A. | 2016年 / American Scientific Publishers卷 / 13期

关键词：

Modified Toeplitz Matrix Method; Nonlinear Algebraic System; Nonlinear Partial Differential Equation of Fractional Order; Nonlinear Volterra Integral Equations of the Second Kind;

D O I：

10.1166/jctn.2016.5323

中图分类号：

学科分类号：

摘要：

In this paper, a set of nonlinear Volterra integral equations (NVIEs) of the second kind, with nonlocal condition is established from a nonlocal nonlinear partial differential equation (NPDE) of fractional order. The existence of a unique solution is guaranteed. Moreover, some properties concerning the stability of the solution are obtained. The modified Toeplitz matrix method (MTMM) is used, as a numerical method, to obtain a nonlinear algebraic system (NAS). In addition, many important theorems related to the existence of a unique solution of the NAS are considered and proved. Finally, numerical results are calculated, and the rate convergence of the error, in each case, is computed. © 2016 American Scientific Publishers All rights reserved.

引用

页码：4580 / 4587

页数：7

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