A generalized moving least square reproducing kernel method

A generalization of moving least square reproducing kernel method is presented in this work. The moving least square reproducing kernel method is obtained by using a moving least square scheme but not in the discrete version. The resulted scheme provides a continuous basis which is able to reproduce any mm-thth order polynomial, and prepares a scheme that can approximate smooth functions with an optimal accuracy. On the other hand, considering the power of moving least square scheme in meshless approximation for the numerical solution of partial differential equations, the generalized moving least square approximation is able to approximate λ(u)λ(u) just in terms of node values where λλ is an arbitrary linear operator. In this paper, a generalization of moving least square reproducing kernel method is presented which employs the generalized version of moving least square method. The method approximates a test functional, based on the values of nodes. The convergence rate of the method is measured in terms of dilation parameter of window function. The method is simpler and faster to implement than the classical ones where it does not use the shape function. Numerical tests are presented to confirm the theoretical results. The numerical results establish the efficiency of the proposed method.