Convergence analysis of an iterative scheme for solving initial value problem for multidimensional partial differential equations

Existence and uniqueness of solutions of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations are proved using Banach fixed-point theorem. An iterative scheme is derived and rigorous convergence analysis of this scheme and an error estimate are included as well. Several numerical examples for high dimensional initial value problem for heat and wave type partial differential equations are presented to demonstrate reliability and performance of proposed iterative scheme.