Laguerre and Touchard Polynomials for Linear Volterra Integral and Integro Differential Equations

Abstract

In this paper, efficient numerical methods are given to solve linear Volterra integral (VI) equations and Volterra Integro differential (VID) equations of the first and second types with exponential, singular, regular and convolution kernels. These methods based on Laguerre polynomials (LPs) and Touchard polynomials (TPs) that convert these equations into a system of linear algebraic equations. The results are compared with one another method and with each other. The results show that these methods are applicable and efficient. In addition, the accuracy of solution is presented and also the calculations and Graphs are done by using matlab2018 program.