Abstract:
In this thesis, we used the double Sumudu decomposition method
to solve linear, nonlinear hyperbolic equations. This method is a
combination of the decomposition method and double Sumudu transform.
In order to check the applicability of this method, five examples
are given. Theta-finite difference method is applied to solve
singular linear, nonlinear hyperbolic equations and coupled system
of hyperbolic equations, five examples are demonstrated to identify
the accuracy of numerical results. The linear singular and coupled
systems of fractional parabolic equations have been solved by the
Crank-Nicolson method, two examples are applied to illustrate the
method. Finally, we compared the exact and numerical solutions.
In order to obtain the numerical solutions, programs of numerical
solutions are written using MATLAB software.
