Iteration scheme for initial value problem for PDEs: Existence, convergence and comparison

TL;DR

This paper reviews existence and uniqueness results for PDE initial value problems, introduces an iterative scheme with error estimates, and demonstrates its application through numerical examples and comparisons to recent results.

Contribution

It presents a new iterative scheme for PDE initial value problems, including error estimates and practical demonstrations, with comparisons to existing methods.

Findings

The iterative scheme converges under certain conditions.

Numerical examples validate the scheme's effectiveness.

Comparison shows advantages over recent methods.

Abstract

Results about existence and uniqueness of solutions of initial value problem for certain types of partial differential equations are recalled as well as iterative scheme and an error estimate for approximate solutions obtained using this scheme. Several numerical examples are presented to demonstrate how the proposed iterative scheme can be applied, with emphasis given to verifying assumptions of using the scheme. Comparison to other recently presented results is done in this respect.