Andang Sunarto^1,*, Praveen Agarwal^2,3,4, Jumat Sulaiman⁵, Jackel Vui Lung Chew⁶

Intelligent Automation & Soft Computing, Vol.31, No.2, pp. 1173-1184, 2022, DOI:10.32604/iasc.2022.020542

Abstract Solving time-fractional diffusion equation using a numerical method has become a research trend nowadays since analytical approaches are quite limited. There is increasing usage of the finite difference method, but the efficiency of the scheme still needs to be explored. A half-sweep finite difference scheme is well-known as a computational complexity reduction approach. Therefore, the present paper applied an unconditionally stable half-sweep finite difference scheme to solve the time-fractional diffusion equation in a one-dimensional model. Throughout this paper, a Caputo fractional operator is used to substitute the time-fractional derivative term approximately. Then, the stability of the difference scheme combining the… More >

Luciano Pereira da Silva^1,*, Bruno Benato Rutyna¹, Aline Roberta Santos Righi², Marcio Augusto Villela Pinto³

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.2, pp. 699-715, 2021, DOI:10.32604/cmes.2021.014239

Abstract In this article, we improve the order of precision of the two-dimensional Poisson equation by combining extrapolation techniques with high order schemes. The high order solutions obtained traditionally generate non-sparse matrices and the calculation time is very high. We can obtain sparse matrices by applying compact schemes. In this article, we compare compact and exponential finite difference schemes of fourth order. The numerical solutions are calculated in quadruple precision (Real * 16 or extended precision) in FORTRAN language, and iteratively obtained until reaching the round-off error magnitude around 1.0E −32. This procedure is performed to ensure that there is no… More >

Muhammad Amin¹, Muhammad Abbas^2,*, Dumitru Baleanu^3,4,5, Muhammad Kashif Iqbal⁶, Muhammad Bilal Riaz⁷

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.1, pp. 361-384, 2021, DOI:10.32604/cmes.2021.012720

Abstract This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes… 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

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 compared based on their computational… More >

Muhammad Saqib¹, Hanifa Hanif^{1, 2}, T. Abdeljawad^{3, 4, 5}, Ilyas Khan^{6, *}, Sharidan Shafie¹, Kottakkaran Sooppy Nisar⁷

CMC-Computers, Materials & Continua, Vol.65, No.3, pp. 1959-1973, 2020, DOI:10.32604/cmc.2020.011339

Abstract The idea of fractional derivatives is applied to several problems of viscoelastic fluid. However, most of these problems (fluid problems), were studied analytically using different integral transform techniques, as most of these problems are linear. The idea of the above fractional derivatives is rarely applied to fluid problems governed by nonlinear partial differential equations. Most importantly, in the nonlinear problems, either the fractional models are developed by artificial replacement of the classical derivatives with fractional derivatives or simple classical problems (without developing the fractional model even using artificial replacement) are solved. These problems were mostly solved for steady-state fluid problems.… More >

Muhammad Ashraf¹, Amir Abbas¹, Saqib Zia², Yu-Ming Chu^{3, 4}, Ilyas Khan^{5, *}, Kottakkaran Sooppy Nisar⁶

CMC-Computers, Materials & Continua, Vol.65, No.2, pp. 1809-1823, 2020, DOI:10.32604/cmc.2020.011404

Abstract The present study is concerned with the physical behavior of the combined effect of nano particle material motion and heat generation/absorption due to the effect of different parameters involved in prescribed flow model. The formulation of the flow model is based on basic universal equations of conservation of momentum, energy and mass. The prescribed flow model is converted to non-dimensional form by using suitable scaling. The obtained transformed equations are solved numerically by using finite difference scheme. For the analysis of above said behavior the computed numerical data for fluid velocity, temperature profile, and mass concentration for several constraints that… 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 stability criteria and order of… More >

Afet Golayoğlu Fatullayev¹, Canan Köroğlu²

CMES-Computer Modeling in Engineering & Sciences, Vol.86, No.1, pp. 39-52, 2012, DOI:10.3970/cmes.2012.086.039

Abstract In this work we solve numerically a boundary value problem for second order fuzzy differential equations under generalized differentiability in the form y''(t) = p(t)y'(t) + q(t)y(t) + F(t) y(0) = γ, y(l) = λ where t ∈T = [0,l], p(t)≥0, q(t)≥0 are continuous functions on [0,l] and [γ]^α = [γ_{_α},γ⁻_α], [λ]^α = [λ_{_α},λ^¯_α] are fuzzy numbers. There are four different solutions of the problem (0.1) when the fuzzy derivative is considered as generalization of the H-derivative. An algorithm is presented and the finite difference method is used for solving obtained problems. The applicability of presented… More >

A. Ja¹, A. Cheddadi¹

FDMP-Fluid Dynamics & Materials Processing, Vol.13, No.4, pp. 235-249, 2017, DOI:10.3970/fdmp.2017.013.235

Abstract This paper reports on the natural convection within a very narrow horizontal annular cavity filled with a porous medium saturated by a binary fluid. The main objective of this study is the identification of the effect of Lewis number on the flow structure and on the heat and mass transfer rates, in a cavity of very small radius ratio R=1.05, in the case of equal buoyancy forces (N=1), for a Rayleigh number Ra=50. The dimensionless governing equations were solved by the centered Finite Difference method using the ADI scheme. Several multicellular flows appear during the variation of the Lewis number,… More >

Ismet Gölgeleyen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.1, pp. 71-90, 2010, DOI:10.3970/cmes.2010.064.071

Abstract In this paper, the solvability conditions for an inverse problem for an integro-differential transport equation are obtained and a numerical approximation method based on the finite difference method is developed. A comparison between the numerical solution and the exact solution of the problem is presented. Experimental results show that proposed method is robust to data noises. More >