Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Explicit Runge-Kutta methods for parabolic partial differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum
SIAM Journal on Scientific Computing
Explicit Difference Schemes with Variable Time Steps for Solving Stiff Systems of Equations
WNAA '96 Proceedings of the First International Workshop on Numerical Analysis and Its Applications
Telescopic projective methods for parabolic differential equations
Journal of Computational Physics
Explicit Time-Stepping for Stiff ODEs
SIAM Journal on Scientific Computing
Patch Dynamics for Multiscale Problems
Computing in Science and Engineering
Numerical stability analysis of an acceleration scheme for step size constrained time integrators
Journal of Computational and Applied Mathematics
Acceleration of lattice Boltzmann models through state extrapolation: a reaction--diffusion example
Applied Numerical Mathematics
Journal of Scientific Computing
A hybrid molecular continuum method using point wise coupling
Advances in Engineering Software
Asymptotic-preserving Projective Integration Schemes for Kinetic Equations in the Diffusion Limit
SIAM Journal on Scientific Computing
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In the context of multiscale computations, techniques have recently been developed that enable microscopic simulators to perform macroscopic level tasks (equation-free multiscale computations). The main tool is the so-called coarse-grained time-stepper, which implements an approximation of the unavailable macroscopic time-stepper using only the microscopic simulator. Several schemes were developed to accelerate the coarse-grained time-stepper, exploiting the smoothness in time of the macroscopic dynamics. To date, mainly the stability of these methods was analyzed. In this paper, we focus on their accuracy properties, mainly in the context of parabolic problems. We study the global error of the different methods, compare with explicit stiff ODE solvers, and use the theoretical results to develop more accurate variants. Our theoretical results are confirmed by various numerical experiments.