An Efficient Local Formulation for Time-Dependent PDEs

In this paper, a local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs. This local approach has flexibility with respect to geometry along with high order of convergence rate. In case of global meshless methods, the two major deficiencies are the computational cost and the optimum value of shape parameter. Therefore, research is currently focused towards localized RBFs approximations, as proposed here. The proposed local meshless procedure is used for spatial discretization, whereas for temporal discretization, different time integrators are employed. The proposed local meshless method is testified in terms of efficiency, accuracy and ease of implementation on regular and irregular domains.