A New Class of Runge-Kutta Methods for Nonlinearly Partitioned Systems

• DOI: 10.48550/arxiv.2401.04859
• Publication Date: 2024-01-01
• Authors: Tommaso Buvoli; Ben S. Southworth
• Keywords: Runge–Kutta methods

This work introduces a new class of Runge-Kutta methods for solving nonlinearly partitioned initial value problems. These methods, named (NPRK), generalize existing additive and component-partitioned allow one to distribute different types implicitness within nonlinear terms. The paper the NPRK framework discusses order conditions, linear stability, derivation implicit-explicit implicit-implicit integrators. concludes with numerical experiments that demonstrate utility viscous Burger's gray thermal radiation transport equations.