Abstract

A CONTINOUS COLLOCATION FORMULATION OF TWO-STEP IMPLICIT BLOCK METHOD FOR SECOND ORDER ODEs USING LEGENDRE BASIS FUNCTION

Folake Lois Joseph

---

The numerical solution of Initial Value Problem of general second order Ordinary Differential Equations have been studied in this work. Implicit two-step continuous multistep method for solving this type of problem has been developed by collocation and interpolation technique. The continuous method which employs Legendre polynomial as basis function yields discrete equivalent as a block method. The main scheme obtained was implemented together with the block formulae for the numerical solution of second order differential equations. Numerical examples are presented to illustrate the applicability and efficiency of the method. The results obtained, when compared with existing methods, are favourable. Keywords: Implicit block method, Legendre basis function, Collocation, Interpolation, Second order ODE

PDF