A. Rasekh^a,*, D.D. Ganji^b, S. Tavakoli^b

Frontiers in Heat and Mass Transfer, Vol.3, No.4, pp. 1-6, 2012, DOI:10.5098/hmt.v3.4.3003

Abstract The present paper deals with the analysis of boundary layer flow and heat transfer of a nanofluid over a stretching circular cylinder in the presence of non-uniform heat source/sink. The governing system of partial differential equations is converted to ordinary differential equations by using similarity transformations, which are then solved numerically using the Runge–Kutta–Fehlberg method with shooting technique. The solutions for the temperature and nanoparticle concentration distributions depend on six parameters, Prandtl number Pr, Lewis number Le, the Brownian motion parameter Nb, the thermophoresis parameter Nt, and non-uniform heat generation/absorption parameters A*, B*. Numerical results are presented both in tabular… More >

M. B. Almatrafi, Abdulghani Alharbi^*

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.1, pp. 827-841, 2023, DOI:10.32604/cmes.2023.027344

Abstract The extraction of traveling wave solutions for nonlinear evolution equations is a challenge in various mathematics, physics, and engineering disciplines. This article intends to analyze several traveling wave solutions for the modified regularized long-wave (MRLW) equation using several approaches, namely, the generalized algebraic method, the Jacobian elliptic functions technique, and the improved Q-expansion strategy. We successfully obtain analytical solutions consisting of rational, trigonometric, and hyperbolic structures. The adaptive moving mesh technique is applied to approximate the numerical solution of the proposed equation. The adaptive moving mesh method evenly distributes the points on the high error areas. This method perfectly and… More >

Abdulghani Ragaa Alharbi^*

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.3, pp. 2193-2209, 2023, DOI:10.32604/cmes.2022.018445

Abstract The Riemann wave system has a fundamental role in describing waves in various nonlinear natural phenomena, for instance, tsunamis in the oceans. This paper focuses on executing the generalized exponential rational function approach and some numerical methods to obtain a distinct range of traveling wave structures and numerical results of the two-dimensional Riemann problems. The stability of obtained traveling wave solutions is analyzed by satisfying the constraint conditions of the Hamiltonian system. Numerical simulations are investigated via the finite difference method to verify the accuracy of the obtained results. To extract the approximation solutions to the underlying problem, some ODE… More >

Kamal Shah^1,2, Hafsa Naz², Thabet Abdeljawad^1,3,*, Aziz Khan¹, Manar A. Alqudah⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 941-955, 2023, DOI:10.32604/cmes.2022.021483

Abstract In this manuscript, an algorithm for the computation of numerical solutions to some variable order fractional differential equations (FDEs) subject to the boundary and initial conditions is developed. We use shifted Legendre polynomials for the required numerical algorithm to develop some operational matrices. Further, operational matrices are constructed using variable order differentiation and integration. We are finding the operational matrices of variable order differentiation and integration by omitting the discretization of data. With the help of aforesaid matrices, considered FDEs are converted to algebraic equations of Sylvester type. Finally, the algebraic equations we get are solved with the help of… More >

Muneerah Al Nuwairan^1,*, Zulqurnain Sabir², Muhammad Asif Zahoor Raja³, Maryam Alnami¹, Hanan Almuslem¹

CMC-Computers, Materials & Continua, Vol.73, No.2, pp. 4441-4454, 2022, DOI:10.32604/cmc.2022.029432

Abstract In this paper, a fractional order model based on the management of waste plastic in the ocean (FO-MWPO) is numerically investigated. The mathematical form of the FO-MWPO model is categorized into three components, waste plastic, Marine debris, and recycling. The stochastic numerical solvers using the Levenberg-Marquardt backpropagation neural networks (LMQBP-NNs) have been applied to present the numerical solutions of the FO-MWPO system. The competency of the method is tested by taking three variants of the FO-MWPO model based on the fractional order derivatives. The data ratio is provided for training, testing and authorization is 77%, 12%, and 11% respectively. The… More >

Zulqurnain Sabir¹, Muhammad Umar¹, Muhammad Asif Zahoor Raja^2,*, Dumitru Baleanu^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 227-251, 2021, DOI:10.32604/cmes.2021.016611

Abstract The presented research aims to design a new prevention class (P) in the HIV nonlinear system, i.e., the HIPV model. Then numerical treatment of the newly formulated HIPV model is portrayed handled by using the strength of stochastic procedure based numerical computing schemes exploiting the artificial neural networks (ANNs) modeling legacy together with the optimization competence of the hybrid of global and local search schemes via genetic algorithms (GAs) and active-set approach (ASA), i.e., GA-ASA. The optimization performances through GA-ASA are accessed by presenting an error-based fitness function designed for all the classes of the HIPV model and its corresponding… More >

H. F. Wong^1,2, Muhammad Sohail³, Z. Siri¹, N. F. M. Noor^1,*

CMC-Computers, Materials & Continua, Vol.68, No.1, pp. 319-336, 2021, DOI:10.32604/cmc.2021.015710

Abstract The mechanism of viscous heating of a Newtonian fluid filled inside a cavity under the effect of an external applied force on the top lid is evaluated numerically in this exploration. The investigation is carried out by assuming a two-dimensional laminar in-compressible fluid flow subject to Neumann boundary conditions throughout the numerical iterations in a transient analysis. All the walls of the square cavity are perfectly insulated and the top moving lid produces a constant finite heat flux even though the fluid flow attains the steady-state condition. The objective is to examine the effects of viscous heating in the fully… More >

Şuayip Yüzbaşı^{1, *}, Murat Karaçayır¹

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.3, pp. 941-956, 2020, DOI:10.32604/cmes.2020.08938

Abstract In this study, we present a numerical scheme similar to the Galerkin method in order to obtain numerical solutions of the Bagley Torvik equation of fractional order 3/2. In this approach, the approximate solution is assumed to have the form of a polynomial in the variable t = x^α , where α is a positive real parameter of our choice. The problem is firstly expressed in vectoral form via substituting the matrix counterparts of the terms present in the equation. After taking inner product of this vector with nonnegative integer powers of t up to a selected positive parameter N,… More >

Mahdi Saedshoar Heris¹, Mohammad Javidi¹, Bashir Ahmad^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.1, pp. 249-272, 2019, DOI:10.32604/cmes.2019.08080

Abstract In this paper, we propose numerical methods for the Riesz space fractional advection-dispersion equations with delay (RFADED). We utilize the fractional backward differential formulas method of second order (FBDF2) and weighted shifted Grünwald difference (WSGD) operators to approximate the Riesz fractional derivative and present the finite difference method for the RFADED. Firstly, the FBDF2 and the shifted Grünwald methods are introduced. Secondly, based on the FBDF2 method and the WSGD operators, the finite difference method is applied to the problem. We also show that our numerical schemes are conditionally stable and convergent with the accuracy of O(k+ h²) and O(k²… More >

Xia Yuan¹, Wu Jichun², Zhou Luying³

The International Conference on Computational & Experimental Engineering and Sciences, Vol.9, No.2, pp. 117-126, 2009, DOI:10.3970/icces.2009.009.117

Abstract This paper establishes a difference approximation on time-space fractional advection-dispersion equations. Based on the difference approximation an ideal numerical example has been solved, and the result is compared with the one of the rigorous time fractional advection-dispersion equation and the rigorous space fractional advection-dispersion equation respectively. The results show: when time fractional order parameter γ=1 or space fractional order parameter α=2, the numerical calculation result of the time-space fractional advection-dispersion equations is in accordance with that of the rigorous time fractional advection-dispersion equation or the rigorous space fractional advection-dispersion equation. The variation law of the result with parameter is also… More >