A GLOBAL ERROR ESTIMATION FOR LINEAR MULTISTEP METHODS FOR NUMERICAL SOLUTION OF NON - STIFF ORDINARY DIFFERENTIAL EQUATIONS

This thesis is mainly concerned with the derivation and an analysis of error of a class of continuous Adains-Moulton schemes with application for a direct solution of non - stiff first order differential equations. The members of the continuous Adams- Moulton methods are constructed by making use of the integrand approximation process, whereby the integrand is left continuous during the integration process. Very high order methods are easily obtained by this approach in contrast to the other derivation approaches based on multistep collocation for this class of methods. We show that for a specified step number K, of finite difference formula can be generated from the continuous formula, by evaluating the latter at some grid points. It is also discovered that these schemes are of order at least K +1 with very close accuracy and stability properties to that of the conventional Adams - Moulton Method of the same step number, which is also a member of this new discrete set of formulae. The K discrete formula are applied simultaneously over successive blocks of meshes for a direct solution of non - stiff initial value problems for first order ordinary differential equations. This is achieved at very little extra computational effort.A global error estimate to the continuous approximation is discussed. We develop an analytical error estimation approach to the method for initial value problems. Numerical examples are included to illustrate the reliability and accuracy of the estimates.