ALGEBRAIC STRUCTURE OF THE WEAK STAGE ORDER CONDITIONS FOR RUNGE-KUTTA METHODS

Document Type

Article

Publication Date

1-1-2024

Abstract

Runge-Kutta (RK) methods may exhibit order reduction when applied to stiff problems. For linear problems with time-independent operators, order reduction can be avoided if the method satisfies certain weak stage order (WSO) conditions, which are less restrictive than traditional stage order conditions. This paper outlines the first algebraic theory of WSO, and establishes general order barriers that relate the WSO of a RK scheme to its order and number of stages for both fully-implicit and DIRK schemes. It is shown in several scenarios that the constructed bounds are sharp. The theory characterizes WSO in terms of orthogonal invariant subspaces and associated minimal polynomials. The resulting necessary conditions on the structure of RK methods with WSO are then shown to be of practical use for the construction of such schemes.

Identifier

85174887074 (Scopus)

Publication Title

SIAM Journal on Numerical Analysis

External Full Text Location

https://doi.org/10.1137/22M1483943

ISSN

00361429

First Page

48

Last Page

72

Issue

1

Volume

62

Grant

2012271

Fund Ref

National Science Foundation

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