Existence and optimality of strong stability preserving linear multistep methods: a duality-based approach
arXiv:1504.039304 citationsh-index: 26
Originality Highly original
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For researchers in numerical ODEs, this provides a theoretical foundation for constructing high-order strong stability preserving methods, which is a fundamental advance.
The authors prove the existence of explicit linear multistep methods of any order with positive coefficients, using a duality-based linear programming approach. This resolves a long-standing open problem in numerical analysis.
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.