Before revision:  Following from recent work on multirate exponential Runge--Kutta (MERK) methods , that construct multirate schemes by approximating the action of matrix \varphi-functions within explicit exponential Runge--Kutta methods, the proposed methods similarly build off of explicit exponential Rosenbrock (ExpRB) methods . By leveraging the exponential Rosenbrock structure, the proposed Multirate Exponential Rosenbrock (MERB) methods  consist of the solution to a sequence of modified ``fast'' initial-value problems, that may themselves be approximated through subcycling any desired IVP solver.
After revision:  Following from recent work on multirate exponential Runge--Kutta (MERK) methods , that construct multirate schemes by approximating the action of matrix \varphi-functions within explicit exponential Runge--Kutta methods, the proposed methods similarly build off of explicit exponential Rosenbrock (ExpRB) methods , thereby called Multirate Exponential Rosenbrock (MERB) methods consist of the solution to a sequence of modified ``fast'' initial-value problems, that may themselves be approximated through subcycling any desired IVP solver.