Accelerated finite difference schemes for second order degenerate elliptic and parabolic problems in the whole space

TL;DR

This paper establishes conditions for accelerating finite difference schemes for degenerate second order elliptic and parabolic equations using Richardson's method, achieving higher convergence orders.

Contribution

It provides a theoretical framework for applying Richardson's method to improve convergence rates of finite difference schemes for degenerate PDEs.

Findings

Sufficient conditions for convergence acceleration are identified.

Richardson's method can be applied to degenerate PDEs.

Higher order convergence is achievable under specified conditions.

Abstract

We give sufficient conditions under which the convergence of finite difference approximations in the space variable of possibly degenerate second order parabolic and elliptic equations can be accelerated to any given order of convergence by Richardson's method.