Solving stiff ordinary differential equation with one simultaneous implicit equation

摘要

With the solution of only m-th simultaneous implicit equations similar to singly diagonally implicit Runge-Kutta method, this paper is devoted to the new discrete format to solve m-th system of stiff ordinary differential equations based on simplex integral. The v-stage new method is A-stable and of order 2v, which order similar to v-stage Kuntzm-Butcher method whereas the later need the solution of mv-th implicit equations. Numerical examples illustrate that.