In this paper we present a novel class of methods for high order accurate integration of multirate systems of ordinary differential equation initial-value problems. 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. In addition to proving how to construct MERB methods from certain classes of ExpRB methods, we provide rigorous convergence analysis of the resulting schemes, and present candidate MERB schemes of orders two through six  . We then present numerical simulations to confirm these theoretical convergence rates, and to compare the efficiency of MERB methods against  recently-introduced multirate MERK and MRI-GARK methods.
In this paper we propose a novel class of methods for high order accurate integration of multirate systems of ordinary differential equation initial-value problems. The proposed methods construct multirate schemes by approximating the action of matrix \varphi-functions within explicit exponential Rosenbrock (ExpRB) methods , thereby called Multirate Exponential Rosenbrock (MERB) methods . They consist of the solution to a sequence of modified "fast" initial-value problems, that may themselves be approximated through subcycling any desired IVP solver. In addition to proving how to construct MERB methods from certain classes of ExpRB methods, we provide rigorous convergence analysis of these methods and derive efficient MERB schemes of orders two through six (the highest order ever constructed infinitesimal multirate methods) . We then present numerical simulations to confirm these theoretical convergence rates, and to compare the efficiency of MERB methods against other recently-introduced high order multirate methods.
R
present
propose
R
Following from recent work on multirate exponential Runge--Kutta (MERK) methods , that
The proposed methods
D
Runge--Kutta methods, the proposed methods similarly build off of explicit exponential
R
. By leveraging the exponential Rosenbrock structure, the proposed
, thereby called
A
. They
R
``fast''
"fast"
R
the resulting schemes, and present candidate
these methods and derive efficient
A
(the highest order ever constructed infinitesimal multirate methods)
A
other
R
multirate MERK and MRI-GARK
high order multirate