A CLASS OF OBRECKHOFF-TYPE METHOD FOR SOLVING SECOND ORDER BOUNDARY VALUE PROBLEMS

Abstract

This work present a class of Obreckhoff-type methods for solving second order Boundary Value Problems (BVPs) with Neuwman and Dirichlet boundary conditions.This is achieved through collocation and interpolation techniques using power series as the basis function. A class of a continuous multi step methods of step number k = 1,2,3 are developed by interpolating the basis function at only two points and collocating the derivative function equation at all the grid points. The methods are implemented in block mode. Analysis of the methods such as order, consistency, zero stability and convergence are examined. Eight problems were solved to determine the efficiency and accuracy of the new method and the numerical solution obtained yielded better results when compared with existing methods