Solution of stiff two point boundary value problems using deferred correction scheme

IBRAHEEM, Kais Ismail, Promotor Prof.Dr.Ir. Prayoto, MSc

2003 | Disertasi | S3 Ilmu Teknik

Dalam disertasi ini akan dibahas aplikasi metode numeris pada suatu kelas stiff two-point boundary value proplems linier, dan orde kedua. Salah satu masalah standar dalam kelas tersebut adalah: (formula), 0

In this dissertation the application of numerical method to a class of a second order, linear, stiff two-point boundary problems was considered. One standard form of such a problem is: (formula) where f, g and s are sufficiently smooth functions on [a,b]. In particular, the interest here is in the solution of these problems for small values of e. The most striking feature of the differential equation is that its order is lower for e = 0 than for e ¹ 0. For this lower order eq uation, one of the two boundary conditions is superfluous. Indeed, for small values of e, it turns out that small regions arise in [a,b], in which the connection with the boundary conditions is made. This causes the solution to have a multiscale character, i.e the solution is described by slowly and rapidly varying parts. This multiscale character is a characteristic feature of the functions that describes the solutions of stiff problems. It also means that attempts to seek a solution in the form of an ascending series in powers of e will fail, unlike the case of regular perturbation problems. Here a NEW approach was used, using the finite difference and deferred correction method known as PASVA (PASo VARiable = variable step in Spanish) in order to solve the above equation. It well know that, the old PASVA was originally designed to solve the non-stiff and mildly stiff problems only. In this work it was shown that its performance for solving extremely stiff problems can be considerably improved by modifying its error estimation and the mesh selection algorithm. The mesh modification was based on modification of f(x). Various and standard applicable examples were implemented in this research using the NEW algorithm of PASVANEW, and the results were obtained indicated that this NEW algorithm is highly effective in solving the linear two-point boundary problems

Kata Kunci : Teknik,Algoritma PASVANEW,Problema Two,Point Boundary Linear