چكيده
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.
