An alternative semi-implicit Euler method for the integration of highly stiff nonlinear differential equations

Abstract

A relatively simple method has been developed for the integration of highly stiff sets of differential equations describing important, noncatalytic, gas-solid reaction systems. the method is based on the semi-implicit Euler scheme which makes it possible to solve the resulting algebraic equations separately with the aid of always converging procedures such as the interval halving or regula falsi. The developed, semi-implicit Euler method has been compared to some implicit and other semi-implicit techniques. Although the proposed procedure is not so effective as the conventional methods in standard stiff situations, it works reliably also under such circumstances when the conventional techniques fail.