Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows
Journal of Computational Physics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations
Recent trends in numerical analysis
Component-Based Derivation of a Parallel Stiff ODE Solver Implemented in a Cluster of Computers
International Journal of Parallel Programming
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
Journal of Computational Methods in Sciences and Engineering - Computational and Mathematical Methods for Science and Engineering Conference 2002 - CMMSE-2002
Grid computing services for parallel algorithms in medicine and biology
MCBC'08 Proceedings of the 9th WSEAS International Conference on Mathematics & Computers In Biology & Chemistry
Grid computing services for parallel algorithms in medicine and biology
WSEAS Transactions on Computers
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Several physical phenomena of great importance in science and engineering are described by large partly stiff differential systems where the stiff terms can be easily separated from the remaining terms. Implicit-Explicit Runge-Kutta (IMEXRK) methods have proven to be useful solving these systems efficiently. However, the application of these methods still requires a large computational effort and their parallel implementation constitutes a suitable way to achieve acceptable response times. In this paper, a technique to parallelize and implement efficiently IMEXRK methods on PC clusters is proposed. This technique has been used to parallelize a particular IMEXRK method and an efficient parallel implementation of the resultant scheme has been derived in a structured manner by following a component-based approach. Several numerical experiments which have been performed on a cluster of dual PCs reveal the good speedup and the satisfactory scalability of the parallel solver obtained.