Abstract:
In recent time, numerous attention from researchers has been engrossed by the various features of the well-known He’s variational iteration method (VIM) and the reconstruction or modified variational iteration method. These methods are more powerful and effective to solve many problems. They provide a sequence which converges to the solution of the problem without discretization of the variables. The key advantage of the current method is that it can expand the convergence area of iterative approximate solutions.
The goal of this thesis is to present an advanced Laplace variational analytical outline, constructed by the Variational Iteration method and Laplace Transform, to solve certain modules of linear and nonlinear differential equations (DEs). Moreover, the method is successfully extended to develop the mathematical model applying the unsteady nonlinear 1D shallow water equations (SWEs) for computing the river depth and velocity flow. An initial solution are carried out to investigate the applicability of the model. Comparison of the result obtained using this method with existing numerical method reveals that the present method is more effective and appropriate for solving the nonlinear shallow water equations.
