Numerical treatment of Kap's equation using a class of fourth order method

Kap's equation is a stiff initial value problem. This paper deals with the treatment of Kap's equation using a class of 4th order explicit Runge-Kutta method. Numerical computation was carried out using Microsoft Visual C++. The results of the computation were found to be highly accurate and consistent with minima errors. A comparison of the results generated from the scheme was also carried out vis-a-vis some other conventional explicit Runge-Kutta formulae. The proposed class of method was found to compare favourably well

Fifth order two-stage explicit Runge-Kutta-Nystrom method for the direct integration of second order ordinary differential equations

In this paper a direct integration of second-order Ordinary Differential Equations (ODEs) of the form using the Explicit Runge-Kutta-Nystrom method with higher derivatives is presented. Various numerical schemes are derived and tested on standard problems. The higher-order explicit Runge-Kutta-Nystrom (HERKN) method given in this paper is compared with the conventional Explicit Runge Kutta (ERK) schemes. Due to the limitation of ERK schemes in handling stiff problems, the extension to higher order derivative is considered. The results obtained show an improvement on ERK schemes