The arithmetic mean method for solving essentially positive systems on a vector computer ^∗

^∗This research was supported by the Ministero della Pubblica Istruzione, Italy.

Abstract

This paper is concerned with a generalization of the arithmetic mean method developed in [3] for solving large “essentially positive” dynamic systems which are asymptotically stable. This method is well suitable for parallel implementation on a multiprocessor system that can execute concurrently different tasks on a few vector processors with shared central memory, such as the CRAY X-MP. A high-level parallelism among independent tasks is obtained using the Cray multitasking. The consistency and the stability of the method are analysed.

Keywords:

• Splitting methods
• parallel computation
• ordinary differential equations

^∗This research was supported by the Ministero della Pubblica Istruzione, Italy.

^∗This research was supported by the Ministero della Pubblica Istruzione, Italy.

Notes

^∗This research was supported by the Ministero della Pubblica Istruzione, Italy.