Solving large systems of linear ordinary differential equations on a vector computer

This paper is concerned with the development, analysis and implementation on a computer consisting of two vector processors of the arithmetic mean method for solving numerically large sparse sets of linear ordinary differential equations. This method has second-order accuracy in time and is stable. The special class of differential equations that arise in solving the diffusion problem by the method of lines is considered. In this case, the proposed method has been tested on the CRAY X-MP/48 utilizing two CPUs. The numerical results are largely in keeping with the theory; a speedup factor of nearly two is obtained. © 1989.