On the Existence Uniqueness and Solution of the Nonlinear Volterra Partial Integro-Differential Equations
On the Existence Uniqueness and Solution of the Nonlinear Volterra Partial Integro-Differential Equations
复制标题
非线性Volterra偏积分微分方程的存在唯一性及其解
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Tari
中科院分区：
文献类型：
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作者：
A. Tari
翻译后摘要：在本文中，我们研究了一种形式的非线性沃尔泰拉偏积分微分方程（NVPIDE）。首先，我们证明了关于NVPIDE解的存在唯一性的一个定理和一些推论。接下来，我们发展了二维约化微分变换方法（RDTM）来求解一类NVPIDE。为此，基于约化微分变换的一些初步结果，我们证明了一些定理，以发展上述方程的RDTM。最后通过数值算例验证了本文方法的准确性。
Abstract: In this paper, we study a form of the nonlinear Volterra partial integro-differential equations (NVPIDEs). First, we prove a theorem and some corollaries about existence and uniqueness of solution of the NVPIDEs. Next, we develop the two-dimensional reduced differential transform method (RDTM) for solving a class of the NVPIDEs. For this purpose, based on some preliminary results of the reduced differential transform, we prove some theorems to develop RDTM for the aforementioned equations. The paper concludes with some numerical examples to demonstrate the accuracy of the presented method.