Multirate Exponential Rosenbrock Methods

In this paper we propose a novel class of methods for high-order accurate integration multirate systems ordinary differential equation initial-value problems. The proposed construct schemes by approximating the action matrix $\varphi$ functions within explicit exponential Rosenbrock (ExpRB) methods, thereby called ExpRB (MERB) methods. They consist solution to sequence modified “fast” problems, which may themselves be approximated through subcycling any desired problem solver. addition proving how MERB from certain classes provide rigorous convergence analysis these and derive efficient orders 2 6 (the highest-order infinitesimal date). We then present numerical simulations confirm theoretical rates compare efficiency against other recently introduced