Dangers of multiple time step methods
Journal of Computational Physics
Barotropic-baroclinic time splitting for ocean circulation modeling
Journal of Computational Physics
MUR8: a multirate extension of the eighth-order Dormand-Prince method
Applied Numerical Mathematics - Special issue on time integration
Implicit-Explicit Parallel Asynchronous Solver of Parabolic PDEs
SIAM Journal on Scientific Computing
A multirate W-method for electrical networks in state-space formulation
Journal of Computational and Applied Mathematics
Multi-Adaptive Galerkin Methods for ODEs I
SIAM Journal on Scientific Computing
Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics
Journal of Computational Physics
Multirate Timestepping Methods for Hyperbolic Conservation Laws
Journal of Scientific Computing
An A Posteriori-A Priori Analysis of Multiscale Operator Splitting
SIAM Journal on Numerical Analysis
Multirate Explicit Adams Methods for Time Integration of Conservation Laws
Journal of Scientific Computing
Analysis of a multirate theta-method for stiff ODEs
Applied Numerical Mathematics
A multirate time integrator for regularized Stokeslets
Journal of Computational Physics
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
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We develop a hybrid implicit and explicit adaptive multirate time integration method to solve systems of time-dependent equations that present two significantly different scales. We adopt an iteration scheme to decouple the equations with different time scales. At each iteration, we use an implicit Galerkin method with a fast time-step to solve for the fast scale variables and an explicit method with a slow time-step to solve for the slow variables. We derive an error estimator using a posteriori analysis which controls both the iteration number and the adaptive time-step selection. We present several numerical examples demonstrating the efficiency of our scheme and conclude with a stability analysis for a model problem.