Numerical solution of some Volterra integrodifferential equations by using collocation methods

Abstract

This thesis aims to present a straightforward, convergent, and readily applicable numerical method for computing approximate solutions to linear two-dimensional first-order and second-order partial Volterra integro-differential equations, along with a class of high-order linear and non-linear partial Volterra integrodifferential equations in two dimensions. We construct algorithms based on Taylor polynomials of two variables to address these equations numerically, and a rigorous convergence analysis with error estimates are discussed in details to validate the convergence of the approximate solution to the exact solution. The theoretical findings are reinforced with several numerical examples to test the efficiency of the proposed scheme and to confirm the reliability of the convergence analysis of the proposed convergent algorithms.