Analysis of Composite Runge Kutta Methods and New One-Step Technique for Stiff Delay Differential Equations

This paper presents fourth order Composite Runge Kutta (RK) methods based on Arithmetic Mean (AM), Harmonic Mean (HaM), Centroidal Mean (CeM), Contraharmonic Mean (CoM) and a new one-step technique which uses non-linear polynomial interpolating function to solve the stiff Delay differential equations (DDEs). The stability polynomials of these methods are derived. The Local Grid Search Algorithm is used to determine the stability regions. The efficiency of these methods is compared through three numerical examples of stiff Delay Differential Equations (DDEs).