IMPLICIT ADAMS TYPE LINEAR MULTISTEP METHOD FOR SOLVING STIFF DIFFERENTIAL EQUATIONS

Abstract

ABSTRACT In this thesis 3-step implicit Adam’s type method for solving linear, non-linear ordinary differential equations and stiff differential system of ODEs were derived through the application of power series expansion collocating at 6 and 9 off-grid points respectively. The Schemes were shown to be consistent and zero-stable, thereby establishing their convergence. Numerical examples solved attested the efficiency and reliability of the Schemes. The block method with 6 off-grid points 1 3 , 2 3 , 4 3 , 5 3 , 7 3 ,𝑎𝑛𝑑 8 3 at collocation has order (11, 11, 11, 11, 11, 11, 11, 11) and the error constants are −11899 349192166400 , −179 5456127600 ,… 5609 1325839006800 . Numerical results obtained show that the methods are competitive in terms of accuracy.