Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

Tranquilli, Paul; Ricketson, Lee; Haut, Terry; Hittinger, Jeffrey

doi:10.1007/s10543-025-01090-9

Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

Journal Article · Wed Nov 19 00:00:00 EST 2025 · BIT Numerical Mathematics

DOI:https://doi.org/10.1007/s10543-025-01090-9· OSTI ID:3010255

^[1]; Ricketson, Lee ^[1]; Haut, Terry ^[1]; Hittinger, Jeffrey ^[1]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC52-07NA27344; SC0023164

OSTI ID:: 3010255

Report Number(s):: LLNL--JRNL-865529

Journal Information:: BIT Numerical Mathematics, Journal Name: BIT Numerical Mathematics Journal Issue: 4 Vol. 65; ISSN 0006-3835; ISSN 1572-9125

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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Related Subjects

Applied Dynamical Systems
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Two-Step Runge-Kutta

Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

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