Existence and optimality of strong stability preserving linear multistep methods: a duality-based approach

TL;DR

This paper proves the existence of explicit linear multistep methods of any order with positive coefficients using a duality-based linear programming approach, advancing theoretical understanding of stability preserving methods.

Contribution

It introduces a duality-based linear programming framework to establish the existence of high-order explicit linear multistep methods with positive coefficients.

Findings

Existence of explicit linear multistep methods of any order with positive coefficients

Development of a duality-based approach for stability analysis

Theoretical advances in stability preserving numerical methods

Abstract

We prove the existence of explicit linear multistep methods of any order with positive coefficients. Our approach is based on formulating a linear programming problem and establishing infeasibility of the dual problem. This yields a number of other theoretical advances.