Browsing by Author "Al-Mdallal, Qasem"

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Citation Count: Rana, Gule;...et.al. "A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models", Journal of Function Spaces, Vol.2022.
A Modified Algorithm Based on Haar Wavelets for the Numerical Simulation of Interface Models
(2022) Rana, Gule; Asif, Muhammad; Haider, Nadeem; Bilal, Rubi; Ahsan, Muhammad; Al-Mdallal, Qasem; Jarad, Fahd; 234808
In this paper, a new numerical technique is proposed for the simulations of advection-diffusion-reaction type elliptic and parabolic interface models. The proposed technique comprises of the Haar wavelet collocation method and the finite difference method. In this technique, the spatial derivative is approximated by truncated Haar wavelet series, while for temporal derivative, the finite difference formula is used. The diffusion coefficients, advection coefficients, and reaction coefficients are considered discontinuously across the fixed interface. The newly established numerical technique is applied to both linear and nonlinear benchmark interface models. In the case of linear interface models, Gauss elimination method is used, whereas for nonlinear interface models, the nonlinearity is removed by using the quasi-Newton linearization technique. The L∞ errors are calculated for different number of collocation points. The obtained numerical results are compared with the immersed interface method. The stability and convergence of the method are also discussed. On the whole, the numerical results show more efficiency, better accuracy, and simpler applicability of the newly developed numerical technique compared to the existing methods in literature.
Citation Count: Abdeljawad, Thabet...et al. (2020). "Efficient sustainable algorithm for numerical solutions of systems of fractional order differential equations by Haar wavelet collocation method", Alexandria Engineering Journal, Vol. 59, No. 4, pp. 2391-2400.
Efficient sustainable algorithm for numerical solutions of systems of fractional order differential equations by Haar wavelet collocation method
(2020) Abdeljawad, Thabet; Amin, Rohul; Shah, Kamal; Al-Mdallal, Qasem; Jarad, Fahd; 234808
This manuscript deals a numerical technique based on Haar wavelet collocation which is developed for the approximate solution of some systems of linear and nonlinear fractional order differential equations (FODEs). Based on these techniques, we find the numerical solution to var-ious systems of FODEs. We compare the obtain solution with the exact solution of the considered problems at integer orders. Also, we compute the maximum absolute error to demonstrate the effi-ciency and accuracy of the proposed method. For the illustration of our results we provide four test examples. The experimental rates of convergence for different number of collocation point is calculated which is approximately equal to 2. Fractional derivative is defined in the Caputo sense. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
Citation Count: Alqudah, Manar A...et al. (2020). "Existence theory and approximate solution to prey–predator coupled system involving nonsingular kernel type derivative", Advances in Difference Equations, Vol. 2020, No. 1.
Existence theory and approximate solution to prey–predator coupled system involving nonsingular kernel type derivative
(2020) Alqudah, Manar A.; Abdeljawad, Thabet; Eiman; Shah, Kamal; Jarad, Fahd; Al-Mdallal, Qasem; 234808
This manuscript considers a nonlinear coupled system under nonsingular kernel type derivative. The considered problem is investigated from two aspects including existence theory and approximate analytical solution. For the concerned qualitative theory, some fixed point results are used. While for approximate solution, the Laplace transform coupled with Adomian method is applied. Finally, by a pertinent example of prey–predator system, we support our results. Some graphical presentations are given using Matlab. © 2020, The Author(s).
Citation Count: Kumar, Pradeep;...et.al. (2023). "Magnetic dipole effects on unsteady flow of Casson-Williamson nanofluid propelled by stretching slippery curved melting sheet with buoyancy force",
Magnetic dipole effects on unsteady flow of Casson-Williamson nanofluid propelled by stretching slippery curved melting sheet with buoyancy force
(2023) Kumar, Pradeep; Nagaraja, Basavarajappa; Almeida, Felicita; AjayKumar, Abbani Ramakrishnappa; Al-Mdallal, Qasem; Jarad, Fahd; 234808
In particular, the Cattaneo-Christov heat flux model and buoyancy effect have been taken into account in the numerical simulation of time-based unsteady flow of Casson-Williamson nanofluid carried over a magnetic dipole enabled curved stretching sheet with thermal radiation, Joule heating, an exponential heat source, homo-heterogenic reactions, slip, and melting heat peripheral conditions. The specified flow's partial differential equations are converted to straightforward ordinary differential equations using similarity transformations. The Runge–Kutta–Fehlberg 4-5th order tool has been used to generate solution graphs for the problem under consideration. Other parameters are simultaneously set to their default settings while displaying the solution graphs for all flow defining profiles with the specific parameters. Each produced graph has been the subject of an extensive debate. Here, the analysis shows that the thermal buoyancy component boosts the velocity regime. The investigation also revealed that the melting parameter and radiation parameter had counterintuitive effects on the thermal profile. The velocity distribution of nanofluid flow is also slowed down by the ferrohydrodynamic interaction parameter. The surface drag has decreased as the unsteadiness parameter has increased, while the rate of heat transfer has increased. To further demonstrate the flow and heat distribution, graphical representations of streamlines and isotherms have been offered.
Citation Count: Khan, Imran...et al. (2022). "On a new method for finding numerical solutions to integro-differential equations based on Legendre multi-wavelets collocation", Alexandria Engineering Journal, Vol. 61, No. 4, pp. 3037-3049.
On a new method for finding numerical solutions to integro-differential equations based on Legendre multi-wavelets collocation
(2022) Khan, Imran; Asif, Muhammad; Amin, Rohul; Al-Mdallal, Qasem; Jarad, Fahd; 234808
In this article, a wavelet collocation method based on linear Legendre multi-wavelets is proposed for the numerical solution of the first as well as higher orders Fredholm, Volterra and Volterra–Fredholm integro-differential equations. The presented numerical method has the capability to tackle the solutions of both linear and nonlinear problems of these model equations. In order to endorse accuracy and efficiency of the method, it is tested on various numerical problems from literature with the aid of maximum absolute errors and rates of convergence. L∞ norms are used to compare the numerical results with other available methods such as Multi-Scale-Galerkin's method, Haar wavelet collocation method and Meshless method from literature. The comparability of the presented method with other existing numerical methods demonstrates superior efficiency and accuracy.
Citation Count: Shah, Kamal;...et.al. (2023). "On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method", CMES - Computer Modeling in Engineering and Sciences, Vol.136, No.2, pp.1457-1472.
On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method
(2023) Shah, Kamal; Abdeljawad, Thabet; Jarad, Fahd; Al-Mdallal, Qasem; 234808
This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using Matlab-16, we simulate the series solution to illustrate our results graphically. Finally, a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.
Citation Count: Ali, Bagh...at all (2021). "Significance of suction/injection, gravity modulation, thermal radiation, and magnetohydrodynamic on dynamics of micropolar fluid subject to an inclined sheet via finite element approach", Case Studies in Thermal Engineering, Vol. 28.
Significance of suction/injection, gravity modulation, thermal radiation, and magnetohydrodynamic on dynamics of micropolar fluid subject to an inclined sheet via finite element approach
(2021) Ali, Bagh; Shafiq, Anum; Siddique, Imran; Al-Mdallal, Qasem; Jarad, Fahd; 234808
This communication explores the significance of suction/injection for gravity modulation mixed convection in micropolar fluid flow due to an inclined sheet in the presence of magnetic field and thermal radiation. In recent years, very extensive modern technological applications have rise the interest in mixed convection controlled by g-jitter forces associated with microgravity. The novelty of the present study is effects of g-jitter on dynamics of micropolar fluid adjustable inclination to the sheet taken into account. Mathematical formulation based on usual laws of conservation is non dimensionalized with emerging parameters through implementation of similarity transform to yield a corresponding set of partial differential equations. In the face of convective non linearity combined with coupling due to mixed convection and micropolarity, a finite element discretization is harnessed to be coded and run on Matlab platform. The credibility of numerical procedure is assured for its acceptable adoption with the established results. The growing strength of amplitude of modulation is showing proportional decrease and increase in the fluctuation of heat transfer and skin friction coefficients, and the fluctuation of reduced skin friction factor, couple stress, and Nusselt number improves with larger inputs of amplitude. These findings would be helpful to experts dealing with upper space heat transportation, performance of materials such as crystals and effectiveness of chemical catalytic reactors.