The aim of this study is to offer a compatible numerical technique to solve second-order linear partial integro-differential equations with variable (functional) bounds, including two independent variables, under the initial and/or boundary conditions by using hybrid Hermite and Taylor series. The method converts the presented integro-differential equation to a matrix equation including the unknown Hermite coefficients. Solving this matrix equation and applying the collocation method, the approximate solution of the problem is obtained in terms of the Hermite polynomials. Also, by means of an error estimation and convergence test related to residual functions, some examples to illustrate the accuracy and efficiency of the method are fulfilled; the obtained results are scrutinized and interpreted. All numerical computations have been performed on the computer programs.

这项研究的目的是提供一种兼容的数值技术，通过使用混合Hermite和泰勒级数，在初始和/或边界条件下求解具有可变（功能）边界（包括两个自变量）的二阶线性偏积分微分方程。该方法将提出的积分微分方程转换为包含未知Hermite系数的矩阵方程。求解该矩阵方程并应用搭配方法，可以根据Hermite多项式获得该问题的近似解。此外，通过与残差函数相关的误差估计和收敛性测试，实现了一些说明该方法的准确性和效率的示例。仔细检查和解释所获得的结果。