Muhammad Saqib¹, Muhammad Shoaib Arif^2,*, Shahid Hasnain³, Daoud S. Mashat⁴

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 2161-2183, 2021, DOI:10.32604/cmc.2021.014507 - 05 February 2021

Abstract The efficiency of solving computationally partial differential equations can be profoundly highlighted by the creation of precise, higher-order compact numerical scheme that results in truly outstanding accuracy at a given cost. The objective of this article is to develop a highly accurate novel algorithm for two dimensional non-linear Burgers Huxley (BH) equations. The proposed compact numerical scheme is found to be free of superiors approximate oscillations across discontinuities, and in a smooth flow region, it efficiently obtained a high-order accuracy. In particular, two classes of higher-order compact finite difference schemes are taken into account and… More >

M. Dehghan¹, M. Abbaszadeh², A. Mohebbi³

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 481-516, 2015, DOI:10.3970/cmes.2015.107.481

Abstract In the current paper the two-dimensional time fractional Klein-Kramers equation which describes the subdiffusion in the presence of an external force field in phase space has been considered. The numerical solution of fractional Klein-Kramers equation is investigated. The proposed method is based on using finite difference scheme in time variable for obtaining a semi-discrete scheme. Also, to achieve a full discretization scheme, the Kansa's approach and meshless local Petrov-Galerkin technique are used to approximate the spatial derivatives. The meshless method has already proved successful in solving classic and fractional differential equations as well as for… More >