Explicit methods in solving stiff ordinary differential equations

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.