Spectral Collocation Method For Solving Higher Order Linear And Non Linear Boundary Value Problems

Abstract

In this thesis, the spectral-collocation method is applied to obtain approximate solution for some types of high order linear and non-linear boundary value problem. It was successfully implemented in matrix argument and Chebyshev polynomial of second kind subjected to recurrence relation. A numerical technique also obtained for high order linear and non-linear boundary value problem is presented. The method combines analytical coordinate transformations with a standard Chebyshev spectral collocation method; it is applicable to linear and nonlinear problems. In examples, we give some comparison between exact and other approximate solution. The obtained numerical results reveal that given method very good approximation than other methods. Three numerical examples are considered to demonstrate the usefulness of the method and to show that the method converges with sufficient accuracy to the exact solution. This method provides very efficiently a convergent series solution form with easily computable coefficients. The obtained results are very effective and convenient.