Chebyshev wavelet collocation method for numerical solution of non-linear partial diferantial equation

In this thesis, Chebyshev wavelet collocation method is firstly introduced and also applied to different important nonlinear partial differential equations as Ginzburg- Landau equation, Korteweg-de Vries equation and etc. This method is compared with the each other and showed that how this method powerfull as well as the Legendre wavelet collocation method. Primarily, the main idea of this method is to provide the convergency in terms of Chebyshev wavelet series. To apply the Chebyshev Wavelet collocation method, firstly the operator matrix needs to derived and then transform the nonlinear partial differential equation into a more easily solvable algebraic system by using these matrices. Once obtaining this algebraic system then it may be solved by using Maple packet program. By applying the Chebyshev wavelet collacation method to Ginzburg Landau, Korteweg-de Vries and the other important equation as it mentioned above, obtaining numerical results are compared with the analytical solutions carefully and the results supported by graphs, illustrated by tables. It is finally pointed out that how the numerical solution approximates to the analytical solution. Moreover, we it is observed that the Chebyshev wavelet collocation method is much more suited for solving nonlinear partial diffrential equations than the Chebyshev Wavelet and Legendre Wavelet collocation method. Consequently, it is concluded that the applicability of this method is more simple with respect to the other techniques and also it is seen that the numerical solution has a much better approach to analytical solution.