A CLASS OF EXPLICIT LINEAR MULTISTEP METHOD FOR DIRECT SOLUTION OF THIRD ORDER INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this thesis, a class of discrete Linear Multistep Methods for Direct Solution of third order initial value problems of Ordinary differential Equations is developed using Taylor series expansion technique. The method is motivated by the variety of application areas of third order Ordinary Differential equations, which include Engineering, Science, Management and Technology. The analysis of the basic properties or the methods were carried out using Boundary Locus method. The result shows that the methods are Consistent, Zero-Stable, and Convergent. The methods are programmed in Fortran Programming Language and used to solve some sample third order initial value problems in Ordinary differential equations to demonstrate the practical feasibility and accuracy of the methods.