چكيده به لاتين
Abstract
This thesis is organized based upon the following papers:
[1] K. Maleknejad and M. Tamamgar, A New Reconstruction of Variational
Iteration Method and Its Application to Nonlinear Volterra Integro-differential
Equations,
[2] M. Tamamgar and K. Maleknejad, Chebyshev Parametric Iteration Method
For Solving The Fredholm Inetgral Equations.
The main of this thesis is based on choosing an auxilairy parameter
in parametric iterative method(PIM) for solving nonlinear Volterra
integro-differential equations. Most of the iterative methods are as subsets
of PIM. Actually, the VIM method which is introduced to solve
nonlinear differential problems is the PIM method with a specific parameter
corresponding to the VIM method but it is more different than
the VIM method in about how to achieve this parameter. Comparing
and superiority of this method with adomian decomposition method is
considered. Here, we review the appropriate basis functions due to the
inhomogeneous part of these equations to reachh the better results. Also
the PIM method is considered by choosing Chebyshev polynomials as
basis (CPIM) for solving Fredholm integral equations and the auxiliary
parameter is obtained by Genetic algorithm(GA).
Keywords: Nonlinear Volterra integro-differential equations, Parametric
iterative method, Auxilairy parameter, Chebyshev parametric iterative
method, Genetic algorithm.
