Abstract

COMPUTATIONAL METHODS FOR HIGHER ORDER LINEAR AND NON ? LINEAR INTEGRO ? DIFFERENTIAL EQUATIONS BY SPLINE COLLOCATION

Gegele, O. A, +Taiwo, O. A , +Uwaheren, O. A and Etuk, M. O

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ABSTRACT n this paper, we present two Spline collocation methods namely standard cubic Spline and non ? polynomial Spline colocation to solve third and fourth order linear and non ? linear integro ? differential equations. Newton Kantorocivh scheme was used to linearize the non- linear term in the case of non linear equation and this leads to an iterative procedure. The resulting system of linear algebric equations are then solved using MAPLE 13. The methods are applied to a few examples to illustrate the accuracy and effectiveness of the methods. Key words: Cubic Spline, Non ? polynomial Spline, Higher order integro ? differential equation, Collocation.

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