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.
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页码：4580 / 4587
页数：7
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