Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using Legendre polynomials
Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using Legendre polynomials
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DOI：
10.1016/j.cam.2012.10.021
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发表时间：
2013-04-01
影响因子：
2.4
通讯作者：
Ordokhani, Y.
中科院分区：
文献类型：
--
作者：
Nemati, S.;Lima, P. M.;Ordokhani, Y.
本文讨论了一类二维非线性沃尔泰拉积分方程的近似解的求法。给出了二维移位勒让德函数的性质。利用积分和乘积的运算矩阵以及配置点，将积分方程的求解归结为非线性代数方程组的求解。得到了有关误差分析的一些结果。我们还考虑了该方法的应用某些偏微分方程的解决方案。包括说明性的例子来证明该技术的有效性和适用性。(C)2012爱思唯尔有限公司版权所有。
In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations is discussed. The properties of two-dimensional shifted Legendre functions are presented. The operational matrices of integration and product together with the collocation points are utilized to reduce the solution of the integral equation to the solution of a system of nonlinear algebraic equations. Some results concerning the error analysis are obtained. We also consider the application of the method to the solution of certain partial differential equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. (C) 2012 Elsevier B.V. All rights reserved.