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A new wavelet method for solving a class of nonlinear partial integro-differential equations with weakly singular kernels
Mathematical Sciences ( IF 0.945 ) Pub Date : 2021-06-10 , DOI: 10.1007/s40096-021-00414-4
Yaser Rostami

This article gives a numerical solution for solving the two-dimensional nonlinear Fredholm–Volterra partial integro-differential equations with boundary conditions with weakly singular kernels. The collocation method has been used for these operational matrices of the Taylor wavelet along with the Newton method to reduce the given partial integro-differential equation to the system of algebraic equations. Error analysis is considered to indicate the convergence of the approximation used in this method. Attaining this purpose, first, two-dimensional Taylor wavelet and then operational matrices should be defined. Regarding the characteristics of the Taylor wavelet, we were obtaining high accuracy of the method. Finally, examples are provided to demonstrate that the proposed method is effective.



中文翻译:

求解一类具有弱奇异核的非线性偏积分微分方程的新小波方法

本文给出了求解具有弱奇异核边界条件的二维非线性 Fredholm-Volterra 偏积分微分方程的数值解。搭配方法已被用于泰勒小波的这些运算矩阵以及牛顿方法,以将给定的偏积分微分方程化简为代数方程组。误差分析被认为是表明该方法中使用的近似的收敛性。为达到此目的,首先应定义二维泰勒小波,然后定义运算矩阵。关于泰勒小波的特性,我们获得了该方法的高精度。最后,通过实例证明所提出的方法是有效的。

更新日期:2021-06-10
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