Automatic intervalwise block partitioning using Adams type method and backward differentiation formula for solving ODEs

Abstract

Most methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differentiation formulas (BDFs) which normally require repeated solution of systems of linear equations with coefficient matrix, I hbJ,where J is the Jacobian matrix as part of a Newton-like iteration on each time step. The matrix operations in the iteration scheme consumes a considerable amount of computational effort. Therefore, in this paper, our objective is to reduce the cost of the iteration scheme by technique of partitioning. The strategy adopted for partitioning is based on block Adams method and block BDF method. Numerical results demonstrates the efficiency of the proposed partitioning in improving both the accuracy and CPU time over traditional stiff methods.