A 4-Step Implicit Collocation Method for Solution of First and Second Order Odes

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Author(s) Z A. Adegboye | I. Aliyu
Pages 644-649
Volume 1
Issue 11
Date November, 2012
Keywords Collocation method, Block method , Continuous interpolant, First and Second Order ODEs
Abstract

The approach of collocation method approximation will be adopted in the derivation of discrete schemes for direct integration second order ordinary differential equation which are combined together to form a block method. The method is extended to the case in which the approximate solution to a second order (special or general), as well as first order Initial Value Problems(IVPs) can be calculated from the same continuous interpolant and is of order five which is A-stable and has an implicit structure for efficient implementation. The method produces simultaneously approximation of the solution of initial value problems at a block of four points (i=1,2,3,4). Numerical results are given to illustrate the performance method.

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