Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Stability analysis of lattice Boltzmann methods
Journal of Computational Physics
Explicit Runge-Kutta methods for parabolic partial differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Implementation aspects of 3D lattice-BGK: boundaries, accuracy, and a new fast relaxation method
Journal of Computational Physics
Acceleration of Lattice-BGK schemes with grid refinement
Journal of Computational Physics
Iterative momentum relaxation for fast lattice-Boltzmann simulations
Future Generation Computer Systems - I. High Performance Numerical Methods and Applications. II. Performance Data Mining: Automated Diagnosis, Adaption, and Optimization
Accelerated Lattice Boltzmann Schemes for Steady-State Flow Simulations
Journal of Scientific Computing
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
An Eulerian description of the streaming process in the lattice Boltzmann equation
Journal of Computational Physics
Telescopic projective methods for parabolic differential equations
Journal of Computational Physics
Journal of Computational Physics
A Stability Notion for Lattice Boltzmann Equations
SIAM Journal on Scientific Computing
Numerical stability analysis of an acceleration scheme for step size constrained time integrators
Journal of Computational and Applied Mathematics
Accuracy analysis of acceleration schemes for stiff multiscale problems
Journal of Computational and Applied Mathematics
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Recently, several methods were proposed to accelerate a time integrator that uses a time step that is small compared to the dominant slow time scales of the dynamics of the system. In this paper, we apply these methods to accelerate a lattice Boltzmann model for the one-dimensional FitzHugh-Nagumo reaction-diffusion system. We compare the projective method [C.W. Gear, I.G. Kevrekidis, Projective methods for stiff differential equations: Problems with gaps in their eigenvalue spectrum, SIAM Journal on Scientific Computing 24 (4) (2003) 1091-1106] proposed by Gear and Kevrekidis to the related multistep scheme [C. Vandekerckhove, D. Roose, K. Lust, Numerical stability analysis of an acceleration scheme for step size constrained time integrators, Journal of Computational and Applied Mathematics 200 (2) (2007) 761-777] that we developed in an earlier paper. It is shown that the acceleration related error obtained with both methods is comparable and small compared to the discretization error of the lattice Boltzmann model itself. Therefore, a substantial speedup can be obtained, essentially without accuracy loss. Furthermore, it is shown that the accuracy obtained with these acceleration schemes is better than the accuracy of the lattice Boltzmann model with a larger time step. Finally, we illustrate that it is straightforward to combine the acceleration methods with traditional time integration tools such as adaptive step size control.