In this study, a matched numerical method based on Hermite and Taylor matrix-collocation techniques is developed to obtain the numerical solutions of a combination of the partial integro-differential equations (PIDEs) under Dirichlet boundary conditions, which involve the nonlinearity, delay and Volterra integral terms. These type equations govern wide variety applications in physical sense. The present method easily constitutes the matrix relations of the linear and nonlinear terms in a considered PIDE, using the eligibilities of the Hermite and Taylor polynomials. It thus directly produces a polynomial solution by eliminating a matrix system of nonlinear algebraic functions gathered from the matrix relations. Besides, the validity and precision of the method are tested on stiff examples by fulfilling several error computations. One can state that the method is fast, validate and productive according to the numerical and graphical results

在这项研究中，开发了一种基于Hermite和Taylor矩阵配置技术的匹配数值方法，以获得Dirichlet边界条件下部分积分微分方程（PIDE）组合的数值解，其中涉及非线性，时滞和Volterra积分项。这些类型方程式在物理意义上支配着各种各样的应用。使用Hermite和Taylor多项式的可取性，本方法可以很容易地在所考虑的PIDE中构成线性和非线性项的矩阵关系。因此，它通过消除从矩阵关系中收集的非线性代数函数的矩阵系统，直接产生多项式解。此外，通过完成几个误差计算，在刚性实例上测试了该方法的有效性和准确性。