Use of mathematical switches to solve differential equation problems

Abstract

Mathematical switches have been used to choose the suitable numerical scheme automatically at every computing step while solving differential equation problems with a multischeme approach. The concept of using mathematical switches in a numerical computation with a multiprocessor computer is feasible. The use of the switches in a multischeme computation yields a more accurate solution than the use of only a single scheme. We examined the use of two mathematical switches, namely, the one of exact error and of truncation error. The numerical results from the use of the former switch confirmed our conjecture that a combined solution of several schemes is indeed more accurate than one of an individual scheme. However, a switch of exact error is not practical and the one of truncation error is not satisfactory. Hence, further study is needed to design more practical and more satisfactory mathematical switches, and to establish the practical value on their use.