Derivation of Explicit 6(4) Pair of Hybrid Methods for Special Second Order Ordinary Differential Equations.

Many physical problems can be modelled using special second order ordinary differential equations. Since someof the second order equations are either hard to be solved analytically or have no analytical solutions, therefore in the past research, there has been a continuous need for numerical methods for solving them. In this paper, the derivation of explicit 6(4) pair of hybrid methods with four stages is considered. For the higher order formula, the derivation is done by imposing the free parameter to increase the size of the interval of absolute stability. This method is implemented in variable step-size in which the lower order formula is used to approximate the local error.Numerical comparisons that have been carried out show that the new method outperforms the existing RungeKutta Nystrom 5(4) pair methodfor solving someoscillatory problems. [ABSTRACT FROM AUTHOR]