Dumitru Baleanu^1,2,3, Mehran Namjoo⁴, Ali Mohebbian⁴, Amin Jajarmi^5,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1147-1163, 2023, DOI:10.32604/cmes.2022.022403 - 27 October 2022

Abstract In the present paper, the numerical solution of Itô type stochastic parabolic equation with a time white noise process is imparted based on a stochastic finite difference scheme. At the beginning, an implicit stochastic finite difference scheme is presented for this equation. Some mathematical analyses of the scheme are then discussed. Lastly, to ascertain the efficacy and accuracy of the suggested technique, the numerical results are discussed and compared with the exact solution. More >

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 >

Yasir Nawaz¹, Muhammad Shoaib Arif ¹, Mairaj Bibi^{2, *}, Javeria Nawaz Abbasi², Umer Javed³, Amna Nazeer²

CMC-Computers, Materials & Continua, Vol.62, No.2, pp. 657-677, 2020, DOI:10.32604/cmc.2020.08584

Abstract Present contribution is concerned with the construction and application of a numerical method for the fluid flow problem over a linearly stretching surface with the modification of standard Gradient descent Algorithm to solve the resulted difference equation. The flow problem is constructed using continuity, and Navier Stoke equations and these PDEs are further converted into boundary value problem by applying suitable similarity transformations. A central finite difference method is proposed that gives third-order accuracy using three grid points. The stability conditions of the present proposed method using a Gauss-Seidel iterative procedure is found using VonNeumann… More >

N. Ananda Reddy^a,*, P. Chandra Reddy^a , M.C. Raju^a , S.V.K.Varma^b

Frontiers in Heat and Mass Transfer, Vol.10, pp. 1-7, 2018, DOI:10.5098/hmt.10.4

Abstract A theoretical investigation has been performed to describe the laminar flow of a rotating fluid past a porous plate in conducting field with variable temperature and variable concentration taking into account the chemical reaction, radiation and Dufour effects. The non-dimensional governing equations are solved numerically by using finite difference scheme. The effects of different physical parameters on velocity, temperature and concentration are presented and discussed with the help of graphs. Also the numerical values for local skin friction, Nusselt number and Sherwood number are recorded and analyzed. Increasing values of heat source parameter results in 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 >

M. Dehghan¹, M. Abbaszadeh², A. Mohebbi³

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 399-444, 2014, DOI:10.3970/cmes.2014.100.399

Abstract In this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis functions (RBFs) collocation methodology. We introduce the moving least squares (MLS) approximation and radial point interpolation method (RPIM) with their shape functions, separately. It should be noted that the shape functions of RPIM unlike the shape functions of the… More >