Two Types Of Regularization Methods For Solving Volterra Integral Equations Of The First Type With Perturbed Data

The kernel function in a Volterra integral equation of the first kind usually has weak singularity,which implies that such integral equation is an ill-posed problem.In this thesis two methods are used to solve the Volterra integral equation of the first kind with perturbed data.The first method is based on the combination of the Legendre collocation method and a regularization strategy.The effectiveness of this method is illustrated by the numerical experiments.In the second method,a homotopy operator is constructed by using the homotopy perturbation technique,and then a first-order iterative scheme and a second-order iterative scheme are proposed,respectively.Numerical examples demonstrate the validity of this method.