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.
