16769

16769

بازسازي روش تغييراتي تكراري و كاربردش در معادلات انتگرال - ديفرانسيل غيرخطي ولترا

كارشناسي ارشد

رياضي كاربردي

مهر 1395

پروفسور خسرو مالك نژاد

رياضي

1395/12/07

1/1/1900 12:00:00 AM

Abstract This thesis is organized based upon the following papers: [1] K. Maleknejad an​d M. Tamamgar, A New Reconstruction of Variational Iteration Method an​d Its Application to Nonlinear Volterra Integro-differential Equations, [2] M. Tamamgar an​d 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 an​d 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 an​d 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.