No abstract

In the numerical solution of boundary-value problems for ordinary differential equations, hnear systems with a partmular block structure are encountered. In this paper two packages of FORTRAN subroutines, COLROW and ARCECO, which use alternate row and column elimination for solving such systems, as discussed by Varah, are described Varah's procedure is stable, and introduces no fillin, that is, reqmres no additional storage To improve its efficiency, use is made of the fact that after each sequence of eliminations a reducible matrix is obtained. In addition, the packages presented treat systems with a more general structure than those considered by Varah. The results of numerical experiments, which demonstrate the effectiveness of the new packages and their superiority over a prevmusly pubhshed code, on a suitably restrmted class of problems, are presented

The software package PDECOL [7] is a popular code among scientists wishing to solve systems of nonlinear partial differential equations. The code is based on a method-of-lines approach, with collocation in the space variable to reduce the problem to a system of ordinary differential equations. There are three principal components: the basis functions employed in the collocation; the method used to solve the system of ordinary differential equations; and the linear equation solver which handles the linear algebra. This paper will concentrate on the third component, and will report on the improvement in the performance of PDECOL resulting from replacing the current linear algebra modules of the code by modules which take full advantage of the special structure of the equations which arise. Savings of over 50 percent in total execution time can be realized.

No abstract

No abstract