A Local Discrete Collocation Method for the Numerical Solution of Mixed Volterra-Fredholm Integral Equations

A Local Discrete Collocation Method for the Numerical Solution of Mixed Volterra-Fredholm Integral Equations

The main purpose of this paper is to describe a computational method for solving nonlinear mixed Volterra-Fredholm integral equations of the second kind. The scheme utilizes the shape functions of the moving least squares (MLS) approximation constructed on distributed nodal points as a basis in the discrete collocation method. The MLS methodology is an eective technique for the approximation of an unknown function that involves a locally weighted least square polynomial fitting. The proposed method is meshless, since it is based upon the scattered data and does not require any background mesh or domain elements. The method is effective and its algorithm can be easily implemented. The validity and eficiency of the new technique are demonstrated through a numerical example.