DIRECT BLOCK METHOD FOR SOLVING SINGULAR PERTUBATION OF LINEAR BOUNDARY VALUE PROBLEMS

Abstract

In this study, we present direct block method of Adams Moulton

type for solving singular perturbation of linear two point boundary value

problem directly. Most of the existence research involving second order

singular linear boundary value problems will reduce the problem to a sys

tem of first order ordinary differential equations (ODEs). This approach

will enlarge the system of first order ODEs and needs more computa

tional work. The advantage of the direct block method in this research

is its ability to obtain the solutions at two points simultaneously, and

also the second order singular perturbation problems will be solved di

rectly without reducing it to first order ODEs. Lagrange interpolation

polynomial was applied in the derivation of the proposed method. The

method will solve singular purturbation linear boundary value problems

together with linear shooting technique using constant step size. The

proposed method is examined by comparing the result with the existing

method. Numerical result shows that the direct block method is more

efficient and accurate compared to the existing method. The proposed di

rect method is suitable for solving singular perturbation linear boundary

value problems.