The numerical approximation for the solution of linear and nonlinear integral equations of the second kind by interpolating moving least squares

In this paper, the interpolating moving least-squares (IMLS) method is discussed. The interpolating moving least square methodology is an effective technique for the approximation of an unknown function by using a set of disordered data. Then we apply the IMLS method for the numerical solution of Volterra–Fredholm integral equations, and finally some examples are given to show the accuracy and applicability of the method.

Keywords:

Moving least-squares method , Volterra-Fredholm integro-differential equations , Error analysis