Numerical solution of second order linear two-point boundry value problem using direct multistep method

In this thesis, direct multistep methods are developed for solving second order linear two-point boundary value problems. The proposed direct multistep methods consist of one point direct method and two point direct block method. These methods are then used together with linear shooting technique in solving second order linear two-point boundary value problems using constant step size. Most of the existing research involving second order linear two-point boundary value problems will reduce the problems to a system of first order ordinary differential equation. This approach will enlarge the system of first order ordinary differential equation and needs more computation work. The advantage of direct multistep methods proposed in this thesis solve second order linear two-point boundary value problems directly without reducing it to first order ordinary differential equation. Moreover, the direct multistep methods are also implemented to solve linear boundary value problems with singular perturbation. The algorithms for solving second order linear two-point boundary value problems and linear boundary value problems with singular perturbation are then executed in programing code which is written in C language. The numerical results showed that the performance of the developed methods gave good results in terms of maximum error and execution time. In conclusion, the proposed methods in this thesis are suitable for solving second order linear two-point boundary value problems and linear boundary value problems with singular perturbation.

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