Implicit extensions of an explicit multirate Runge–Kutta scheme

Journal Article · 28 December 2021 · Applied Mathematics Letters

DOI: https://doi.org/10.1016/j.aml.2021.107871 · OSTI ID:1883232

Constantinescu, Emil M.  ^[1]

---

1. Argonne National Lab. (ANL), Argonne, IL (United States)

In this work, we propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods. We develop extensions of order one and two with different stability properties on the implicit side. The method is suitable for time-stepping adaptive mesh refinement PDE discretizations with different degrees of stiffness. A numerical example with an advection-diffusion problem illustrates the new method's properties.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 1883232
• Journal Information: Applied Mathematics Letters, Journal Name: Applied Mathematics Letters Vol. 128; ISSN 0893-9659
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English