Numerical solution of sigularly perturbed parabolic problems by a local kernel-based method with an adaptive algorithm

Global approaches make troubles and deficiencies for solving singularly perturbed problems. In this work, a local kernel-based method is applied for solving singularly perturbed parabolic problems. The kernels are constructed by the Newton basis functions (NBFs) on stencils selected as thin regions of the domain of problem that leads to increasing accuracy with less computational costs. In addition, position of nodes may affect significantly on accuracy of the method, therefore, the adaptive residual subsampling algorithm is used to locate optimal position of nodes. Finally, some problems are solved by the proposed method and the accuracy and efficiency of the method is compared with results of some other methods.

Keywords:

Local kernel-based method , Newton basis functions , adaptive residual subsampling algorithm , singularly perturbed parabolic problems , convection-diffusion problems