Explicit methods in solving stiff ordinary differential equations

Abstract

In this article, we extended the existing explicit Taylor method and modified it to gain a new explicit Taylor-liked method in solving stiff differential equations. We also considered the stability property for this method since the stability property of the classical explicit fourth order Runge-Kutta (RK4) method is not adequate for the solution of stiff problems. Implicit methods could work well for stiff problems but have certain drawbacks especially when discussing about the cost. A comparison of the existing implicit Adam-Bashforth, the classical explicit (RK4) and the new explicit Taylor-liked method is presented.