The effect of partial pivoting in sparse ordinary differential equation solvers

AbstractThis paper considers the effect of partial pivoting in automatic ordinary differential equation solvers that utilize sparse matrix techniques. Two solvers are considered, the well-known LSODES solver and a derivate LSOD28. LSODES uses the Yale Sparse Matrix Package which does not perform partial pivoting. LSOD28 uses the MA28 Sparse Matrix Package which does perform partial pivoting. Results are presented for a benchmark problem that contains several features typically present in realistic problems. The results demonstrate that both solvers perform satisfactorily. At the same time, they illustrate that the lack of partial pivoting does not necessarily degrade the efficiency or the reliability of a solver such as LSODES for such problems. They support the argument that partial pivoting is not necessarily required in adaptive sparse solvers to solve complex problems accurately and efficiently