Stabilized explicit peer methods with parallelism across the stages for stiff problems

Abstract

In this manuscript, we propose a new family of stabilized explicit parallelizable peer methods for the solution of stiff Initial Value Problems (IVPs). These methods are derived through the employment of a class of preconditioners proposed by Bassenne et al. (2021) [5] for the construction of a family of linearly implicit Runge-Kutta (RK) schemes.

In this paper, we combine the mentioned preconditioners with explicit two-step peer methods, obtaining a new class of linearly implicit numerical schemes that admit parallelism on the stages. Through an in-depth theoretical investigation, we set free parameters of both the preconditioners and the underlying explicit methods that allow deriving new peer schemes of order two, three and four, with good stability properties and small Local Truncation Error (LTE). Numerical experiments conducted on Partial Differential Equations (PDEs) arising from application contexts show the efficiency of the new peer methods proposed here, and highlight their competitiveness with other linearly implicit numerical schemes.