@Article{cmes.2015.108.375,
AUTHOR = {H. Rafieayan Zadeh, M. Mohammadi, E. Babolian},
TITLE = {Solving a Class of PDEs by a Local Reproducing Kernel Method with An Adaptive Residual Subsampling Technique},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {108},
YEAR = {2015},
NUMBER = {6},
PAGES = {375--396},
URL = {http://www.techscience.com/CMES/v108n6/27286},
ISSN = {1526-1506},
ABSTRACT = {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.},
DOI = {10.3970/cmes.2015.108.375}
}