Second-Derivative Two-Step Mono-Implicit Runge-Kutta Method for Stiff ODEs

Abstract

The study explores a specific class of Second Derivative Two-step mono-implicit Runge-Kutta (SDTSMIRKs) methods within a fixed step-size environment. This method is implemented as one step method in high dimension, addressing the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The p and q denote the order of the input and output methods respectively. Numerical results from linear and non-linear stiff systems demonstrate that the newly proposed methods surpass certain existing methods in the literature.