TY  - EJOU
AU  - Zadeh, H. Rafieayan 
AU  - Mohammadi, M. 
AU  - Babolian, E. 

TI  - Solving a Class of PDEs by a Local Reproducing Kernel Method with An Adaptive Residual Subsampling Technique
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2015
VL  - 108
IS  - 6
SN  - 1526-1506

AB  - A local reproducing kernel method based on spatial trial space spanned by the Newton basis functions in the native Hilbert space of the reproducing kernel is proposed. It is a truly meshless approach which uses the local sub clusters of domain nodes for approximation of the arbitrary field. It leads to a system of ordinary differential equations (ODEs) for the time-dependent partial differential equations (PDEs). An adaptive algorithm, so-called adaptive residual subsampling, is used to adjust nodes in order to remove oscillations which are caused by a sharp gradient. The method is applied for solving the Allen-Cahn and Burgers’ equations. The numerical results show that the proposed method is efficient, accurate and be able to remove oscillations caused by sharp gradient.
KW  - Local reproducing kernel method
KW  -  method of lines
KW  -  Newton basis functions
KW  -  adaptive residual subsampling algorithm

DO  - 10.3970/cmes.2015.108.375