4296

4296

حل عددي معادلات انتگرالي با استفاده از پيش حالت سازها و دستگاه معادلات انتگرالي با استفاده از توابع پايه اي متعامد قطعه اي پيوسته

دكتري

رياضي

1383

دكتر خسرو مالك نژاد

02

In this thesis, we introduce the iterative methods for the solution of the resultinq systems arise from integral equations and partial differential equations. Since the resulting systems from integral equations are ill-conditioned, we use preconeditioned conjugate gradient method with different preconditioners. Therefore, this new system becomes wellconditioned and the complexity of computational operations are reduced and the rate of convergence are increased. In the next section, piecewise continuous orthogonal basic rationalized Haar functions are considered; moreover, the quantities such as operational matrices of integration and product are obtained. Then by means of the above functions, the integral equations and the system are solved. With the application of rationalized Haar functions and the use of Newton-Cotes nodes, the storage of computations is reduced considerably, and the numerical results have a good degree of accuracy. For showing the efficiency of numerical methods we apply the numerical alghorithms for examples and comparing them with analytical solutions.