LEAST SQUARES INTEGRATION-BASED RBF METHOD FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS

In this paper, the method of least square and the recently developed integrationbased radial basis function method are applied for solving partial differential equations. Several boundary value problems defined in rectangular and L-shaped domains with uniform and random nodes are studied. Superiorities like higher accuracy and convergency are shown through comparisons with existing results. Furthermore, a two-dimensional Burgers’ equation is taken as an example to indicate the superior stability and higher accuracy of this proposed method. Numerical results demonstrate that our method works better than classical Kansa’s method and adaptive meshing technique.