Parallel Iterative Solvers for Boundary Value Methods
نویسنده
چکیده
A parallel variant of the block Gauss-Seidel iteration for the solution of block-banded linear systems is presented. The coefficient matrix is partitioned among the processors ss in the domain decomposition methods and then it is split so that the resulting iterative method has the same spectral properties of the block Gauss-Seidel iteration. The parallel algorithm is applied to the solution of block-banded linear systems arising from the numerical discretization of initial value problems by means of Boundary Value Methods (BVMs). BVMs define a new approach for the solution of ordinary differential equations and seem to be attractive for their interesting stability properties and a possible parallel implementation. In this paper, we refer to BVMs based on the extended trapezoidal rules. Keywords-Iterative solvers, Gauss-Seidel iteration, Parallel algorithms, Initial value problems, Boundary value methods.
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