Nasser Sweilam¹, Seham Al-Mekhlafi^2,*, Aya Ahmed³, Ahoud Alsheri⁴, Emad Abo-Eldahab³

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.2, pp. 1619-1645, 2024, DOI:10.32604/cmes.2024.047896 - 20 May 2024

Abstract In this paper, two crossover hybrid variable-order derivatives of the cancer model are developed. Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators. The existence, uniqueness, and stability of the proposed model are discussed. Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models. Comparative studies with generalized fifth-order Runge-Kutta method are given. Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented. We have showcased the efficiency of the proposed More >

Prasantha Bharathi Dhandapani¹, Dumitru Baleanu^2,3,4,*, Jayakumar Thippan¹, Vinoth Sivakumar¹

Computer Systems Science and Engineering, Vol.37, No.3, pp. 331-346, 2021, DOI:10.32604/csse.2021.015619 - 08 March 2021

Abstract In this research, we propose a new change in classical epidemic models by including the change in the rate of death in the overall population. The existing models like Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) include the death rate as one of the parameters to estimate the change in susceptible, infected and recovered populations. Actually, because of the deficiencies in immunity, even the ordinary flu could cause death. If people’s disease resistance is strong, then serious diseases may not result in mortalities. The classical model always assumes a closed system where there is no new birth… More >

P.S.S. Nagalakshm^*, N. Vijaya

Frontiers in Heat and Mass Transfer, Vol.14, pp. 1-9, 2020, DOI:10.5098/hmt.14.4

Abstract In the present investigation is to magnetohydrodymaics (MHD) radiative flow of an incompressible steady flow of Carreau nanofluid explored with carbon nanotubes. The boundary layer flow and heat transfer to a Carreau nanofluid model over a non- linear stretching surface is introduced. The Carreau model, adequate for many non-Newtonian fluids is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical values of the power law exponent n. The modeled boundary layer conservation equations are converted to non-linear coupled ordinary differential equations by a suitable… More >

M. H. T. Alshbool¹, W. Shatanawi^{2, 3, 4, *}, I. Hashim⁵, M. Sarr¹

CMC-Computers, Materials & Continua, Vol.64, No.1, pp. 63-80, 2020, DOI:10.32604/cmc.2020.09431 - 20 May 2020

Abstract One of the most attractive subjects in applied sciences is to obtain exact or approximate solutions for different types of linear and nonlinear systems. Systems of ordinary differential equations like systems of second-order boundary value problems (BVPs), Brusselator system and stiff system are significant in science and engineering. One of the most challenge problems in applied science is to construct methods to approximate solutions of such systems of differential equations which pose great challenges for numerical simulations. Bernstein polynomials method with residual correction procedure is used to treat those challenges. The aim of this paper… More >

Xiaojing Liu¹, Jizeng Wang^1,2, Youhe Zhou^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.3, pp. 225-238, 2013, DOI:10.32604/cmes.2013.094.225

Abstract A wavelet method is proposed for solving a class of nonlinear timedependent partial differential equations. Following this method, the nonlinear equations are first transformed into a system of ordinary differential equations by using the modified wavelet Galerkin method recently developed by the authors. Then, the classical fourth-order explicit Runge-Kutta method is employed to solve the resulting system of ordinary differential equations. To justify the present method, the coupled viscous Burgers’ equations are solved as examples, results demonstrate that the proposed wavelet algorithm have a much better accuracy and efficiency than many existing numerical methods, and More >

Hung-Chang Lee¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.041.001

Abstract The group-preserving schemes developed by Liu (2001) for integrating ordinary differential equations system were adopted the Cayley transform and Padé approximants to formulate the Lie group from its Lie algebra. However, the accuracy of those schemes is not better than second-order. In order to increase the accuracy by employing the group-preserving schemes on ordinary differential equations, according to an efficient technique developed by Runge and Kutta to raise the order of accuracy from the Euler method, we combine the Runge-Kutta method on the group-preserving schemes to obtain the higher-order numerical methods of group-preserving type. They More >

Chein-Shan Liu, Yu-Ling Ku

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 151-178, 2005, DOI:10.3970/cmes.2005.009.151

Abstract In this paper we are concerned with the integration of a semi-discretized version of the Landau-Lifshitz equation, which is fundamental to describe the magnetization dynamics in micro/nano-scale magnetic systems. The resulting ordinary differential equations at the interior grid points are numerically integrated by a combination of the group preserving scheme derived by Liu (2004a) and the fourth-order Runge-Kutta method, abbreviated as GPS-RK4. The new method not only conserves the magnetization magnitude and has the fourth-order accuracy, but also preserves the Lyapunov property of the Landau-Lifshitz equation, namely the free energy is decreasing with time. In More >