Linear Recursive Schemes Associated with Some Nonlinear Partial Differential Equations in One Dimension and the Tau Method

Abstract

Standard compactness arguments for Volterra’s equation are used to prove the existence of the solution of some nonlinear partial differential equations in one dimension by associating them to linear recursive schemes. Sufficient conditions for the quadratic convergence of hyperbolic and parabolic types are given in this paper. By using a best approximation perturbation technique—the Tau Method—we show that these recursive schemes lead to accurate numerical approximations in concrete problems.