A Large-Grained Parallel Solver for Linear Simultaneous Ordinary Differential Equations based on Matrix Exponential and its Evaluation(Application,Algorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2009)

Abstract

We consider an application of the Krylov approximation method for the matrix exponential to the solution of linear simultaneous ordinary differential equations. Although this approach has large-grain parallelism, it has two potential problems, namely, the instability due to a large dimension of the Krylov subspace and the determination of an appropriate dimension of the Krylov subspace. In this paper, we show how to solve these problems. The resulting method is shown to be faster than the implicit finite difference method when the required accuracy is relatively high.