Moving least square for systems of integral equations

Modified moving least squares method for two-dimensional linear and nonlinear systems of integral equations

“…The convergence analysis of the method in matrix norm has been investigated for the systems of one and two-dimensional Fredholm integral equations by authors of [22]. It should be noted that The convergence analysis of the method for implementation classic moving least squares approximation method on a system of integral equations has been discussed and it should be investigated for modified Mls method.…”

“…Using this approach some new methods such as meshless local boundary integral equation method [19], Boundary Node Method (BNM) [20], moving least square reproducing polynomial meshless method [21] and other relative methods are constructed. The new class of meshless methods has been developed which only relied on a set of nodes without the need for an additional mesh in the solution of a one-dimensional system of integral equations [22].…”

“…The Moving Least Square (MLS) method is a feasible numerical approximation method that is an extension of the least squares method, also it is the component of the class of meshless schemes that have a highly accurate approximation. The MlS approximation method is a popular method used in the many meshless methods [12,19,21,22,29,30]. In many procedures used to construct the MLS shape function is used support-domain concept.…”