Convergence for PDEs with an arbitrary odd order spatial derivative term

TL;DR

This paper analyzes the convergence rates of finite difference schemes for linear PDEs involving arbitrary odd order spatial derivatives, establishing convergence for various initial data smoothness levels.

Contribution

It provides the first comprehensive analysis of convergence rates for finite difference schemes applied to PDEs with arbitrary odd order derivatives.

Findings

Convergence rates of first or second order are proven for smooth and less smooth initial data.

The paper extends existing theory to PDEs with higher odd order derivatives.

Finite difference schemes are shown to be effective for these complex PDEs.

Abstract

We compute the rate of convergence of forward, backward and central finite difference $\theta$-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and less smooth initial data.