Solving Second Order Delay Differential Equations directly by a Four-step Multi-Hybrid Block Method

Abstract

The aim of this paper is to compute the numerical solution of special second order delay differential equations directly by a four-step multi-hybrid block method. The methods were generated using collocation and interpolation approach by means of a combination of power series and exponential function at some selected grid and off-grid points. The developed schemes and its first derivatives was combined to form block methods to concurrently solve special second order delay differential equations directly without reducing it to the system of first order. The basic properties of the methods such as order, error constants, consistency and convergence were examined. The developed methods were applied to solve some second order delay differential equations, the methods also solve application problem in other to test for the efficiency and accuracy of the methods. The results are displays in the tables. JEL classification numbers: 65L05; 65L06; 65L20. Keywords: Multi-Hybrid Block Method; Special Second Order Delay Differential Equations; Convergence; Four-step Block Method; Order seventeen.