Iteration scheme for initial value problem for PDEs: Existence, convergence and comparison
For researchers working on numerical solutions of PDEs, this provides an iterative scheme with theoretical guarantees, though the contribution appears incremental.
The paper recalls existence and uniqueness results for initial value problems of certain PDEs, proposes an iterative scheme with error estimates, and demonstrates its application through numerical examples, comparing with recent results.
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.