On The Numerical Solutions For The Initial Value Problems In O.D.E. Using Spline Functions

Abstract

he main purpose o this work is to try to find a new technique for the solution of the third order initial value problem y" = F(x,y) under certain initial cond ions using spline polynomials of degree 7 and 8 s The thesis consists of five chapters Chapter I is a general introduction in which we review some published results concerning the spline approximations for initial value problems In chapter IM, an approximate procedure is introduced to solve the differential equation under consideration sing spline polynomials of degree m, deficiency 4,ie., S()e(" [0,h], we prove the existence and ariqueness of the solution for this equation Also we prove the stability for this method which is stable for m-7,8, I unstable and hence divergent for m29,