Solving initial value problems by the Picard-Chebyshev method with NVIDIA GPUS
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Combining the Picard method with Chebyshev polynomials, we can solve a large number of initial value problems using parallel computation. We develop a matrixvector form of Picard-Chebyshev method and implement it using a NVIDIA graphics card. The algorithm is developed in the NVIDIA CUDA environment and utilize the CUBLAS toolbox. Compared with ODE45 (the Runge-Kutta 45 algorithm implemented in MATLAB), the speedup from using Picard-Chebyshev method for the exemplar problem is about a factor of 30 to 120. Compared with a CPU version of the Picard-Chebyshev algorithm implemented in MATLAB, the speedup from using one NVIDIA graphics card is about a factor of 2 to 3. These results show that even with the simplest utilization of graphical processing units presently available, the speedup with parallel implementations of the Picard-Chebyshev algorithm is up to two order of magnitude.
author list (cited authors)
Bai, X., & Junkins, J. L.