Computational methods for higher order linear and non linear integro differential equations by collocation

Abstract

In this paper, we present two spline collocation methods namely standard cubic spline and non- polynomial spline collocation to solve third and fourth order linear and non-linear integro differential equations. Newton Kantorovich 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 algebraic equations are the solved using Maple 13. The methods are applied to few examples to illustrate the accuracy and effectiveness of the methods.