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 system of first order ordinary differential equations (ODEs). This approach will enlarge the system of first order ODEs and needs more computational 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 directly 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 direct method is suitable for solving singular perturbation linear boundary value problems.