Mumtaz Khan^1,*, Muhammad Shoaib Anwar², Mudassar Imran³, Amer Rasheed⁴

Frontiers in Heat and Mass Transfer, Vol.22, No.5, pp. 1399-1419, 2024, DOI:10.32604/fhmt.2024.056597 - 30 October 2024

Abstract This study employs the Buongiorno model to explore nanoparticle migration in a mixed convection second-grade fluid over a slendering (variable thickness) stretching sheet. The convective boundary conditions are applied to the surface. In addition, the analysis has been carried out in the presence of Joule heating, slips effects, thermal radiation, heat generation and magnetohydrodynamic. This study aimed to understand the complex dynamics of these nanofluids under various external influences. The governing model has been developed using the flow assumptions such as boundary layer approximations in terms of partial differential equations. Governing partial differential equations are… More >

Muhammad Shoaib Arif^1,2,*, Kamaleldin Abodayeh¹, Yasir Nawaz²

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.2, pp. 1213-1241, 2024, DOI:10.32604/cmes.2024.054819 - 27 September 2024

Abstract Fractal time-dependent issues in fluid dynamics provide a distinct difficulty in numerical analysis due to their complex characteristics, necessitating specialized computing techniques for precise and economical solutions. This study presents an innovative computational approach to tackle these difficulties. The main focus is applying the Fractal Runge-Kutta Method to model the time-dependent magnetohydrodynamic (MHD) Newtonian fluid with rescaled viscosity flow on Riga plates. An efficient computational scheme is proposed for handling fractal time-dependent problems in flow phenomena. The scheme is comprised of three stages and constructed using three different time levels. The stability of the scheme… More >

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 >

Ala Kana, Imtiaz Ahmad^*

CMC-Computers, Materials & Continua, Vol.76, No.3, pp. 3443-3464, 2023, DOI:10.32604/cmc.2023.040775 - 08 October 2023

Abstract A newly proposed competent population-based optimization algorithm called RUN, which uses the principle of slope variations calculated by applying the Runge Kutta method as the key search mechanism, has gained wider interest in solving optimization problems. However, in high-dimensional problems, the search capabilities, convergence speed, and runtime of RUN deteriorate. This work aims at filling this gap by proposing an improved variant of the RUN algorithm called the Adaptive-RUN. Population size plays a vital role in both runtime efficiency and optimization effectiveness of metaheuristic algorithms. Unlike the original RUN where population size is fixed throughout… More >

Zulqurnain Sabir¹, Abeer S. Alnahdi^2,*, Mdi Begum Jeelani², Mohamed A. Abdelkawy^2,3,*, Muhammad Asif Zahoor Raja⁴, Dumitru Baleanu^5,6, Muhammad Mubashar Hussain⁷

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.2, pp. 763-785, 2022, DOI:10.32604/cmes.2022.018496 - 14 March 2022

Abstract The present investigations are associated with designing Morlet wavelet neural network (MWNN) for solving a class of susceptible, infected, treatment and recovered (SITR) fractal systems of COVID-19 propagation and control. The structure of an error function is accessible using the SITR differential form and its initial conditions. The optimization is performed using the MWNN together with the global as well as local search heuristics of genetic algorithm (GA) and active-set algorithm (ASA), i.e., MWNN-GA-ASA. The detail of each class of the SITR nonlinear COVID-19 system is also discussed. The obtained outcomes of the SITR system are More >

Ayman Abd-Elhamed^1,2,*, Mohamed Fathy³, Khaled M. Abdelgaber¹

CMC-Computers, Materials & Continua, Vol.71, No.2, pp. 2175-2190, 2022, DOI:10.32604/cmc.2022.021899 - 07 December 2021

Abstract The capability of piles to withstand horizontal loads is a major design issue. The current research work aims to investigate numerically the responses of laterally loaded piles at working load employing the concept of a beam-on-Winkler-foundation model. The governing differential equation for a laterally loaded pile on elastic subgrade is derived. Based on Legendre-Galerkin method and Runge-Kutta formulas of order four and five, the flexural equation of long piles embedded in homogeneous sandy soils with modulus of subgrade reaction linearly variable with depth is solved for both free- and fixed-headed piles. Mathematica, as one of More >

R. Manjula Devi¹, M. Premkumar², Pradeep Jangir³, Mohamed Abdelghany Elkotb^4,5, Rajvikram Madurai Elavarasan⁶, Kottakkaran Sooppy Nisar^7,*

CMC-Computers, Materials & Continua, Vol.70, No.3, pp. 4803-4827, 2022, DOI:10.32604/cmc.2022.020847 - 11 October 2021

Abstract Optimization is a key technique for maximizing or minimizing functions and achieving optimal cost, gains, energy, mass, and so on. In order to solve optimization problems, metaheuristic algorithms are essential. Most of these techniques are influenced by collective knowledge and natural foraging. There is no such thing as the best or worst algorithm; instead, there are more effective algorithms for certain problems. Therefore, in this paper, a new improved variant of a recently proposed metaphorless Runge-Kutta Optimization (RKO) algorithm, called Improved Runge-Kutta Optimization (IRKO) algorithm, is suggested for solving optimization problems. The IRKO is formulated… 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 >

Hao Zhu^1,*, Mulan Wang², Kun Liu², Weiye Xu³

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1799-1811, 2021, DOI:10.32604/cmc.2020.012706 - 26 November 2020

Abstract In order to solve the problem of complicated Non-Uniform Rational B-Splines (NURBS) modeling and improve the real-time performance of the high-order derivative of the curve interpolation process, the method of NURBS modeling based on the slicing and layering of triangular mesh is introduced. The research and design of NURBS curve interpolation are carried out from the two aspects of software algorithm and hardware structure. Based on the analysis of the characteristics of traditional computing methods with Taylor series expansion, the Adams formula and the Runge-Kutta formula are used in the NURBS curve interpolation process, and 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 >