Analysis Of Multistep Methods For Numerical Solution Of Ordinary Differential Equations With Applications

Abstract

This Thesis Provides A Practical Overview Of Multistep Methods For Numerical Solution Of Ordinary Differential Equations. A Multistep Method Is Used For Numerical Solution Of Some Ordinary Differential Equations. The Approach Is To Obtain Multiple Finite Difference Methods (Mfdms) Which Are Combined As Simultaneous Numerical Integrators To Form Some Block Methods Where, The Stability And Convergence Of The Block Methods Are Investigated. We Also Compare Their Performance With Some Single Steps. The Study Shows That The Methods Are Zero-Stable, Consistent And Convergent. These Are Proven By Using Related Theorems Such As Stone-Weierstrass Theorem. The Study Also Enables Us To Investigate The Method With Larger Stability Region. The Block Methods Derived Are Tested To Illustrate The Accuracy And Efficiency Of The Method.