One-step and extrapolation methods for differential- algebraic systems
Numerische Mathematik
Asymptotic error expansions for stiff equations: the implicit Euler scheme
SIAM Journal on Numerical Analysis
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
An implicit-explicit approach for atmospheric transport-chemistry problems
Applied Numerical Mathematics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
On the stability of implicit-explicit linear multistep methods
Applied Numerical Mathematics - Special issue on time integration
Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations
Recent trends in numerical analysis
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
Journal of Computational Physics
Error Analysis of IMEX Runge-Kutta Methods Derived from Differential-Algebraic Systems
SIAM Journal on Numerical Analysis
Semi-Lagrangian multistep exponential integrators for index 2 differential-algebraic systems
Journal of Computational Physics
Proceedings of the first international workshop on High performance computing, networking and analytics for the power grid
Extrapolated Multirate Methods for Differential Equations with Multiple Time Scales
Journal of Scientific Computing
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
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This paper constructs extrapolated implicit-explicit time stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods are based on Euler steps and can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method-of-lines framework. Implicit-explicit schemes based on extrapolation are simple to construct, easy to implement, and straightforward to parallelize. This work establishes the existence of perturbed asymptotic expansions of global errors, explains the convergence orders of these methods, and studies their linear stability properties. Numerical results with stiff ODE, DAE, and PDE test problems confirm the theoretical findings and illustrate the potential of these methods to solve multiphysics multiscale problems.