Article
Mathematics, Applied
Chulkwang Kwak, Christopher Maulen
Summary: In this paper, we analyze the Cauchy problem for the (abcd)-Boussinesq system on one- and two-dimensional Euclidean spaces. We establish the ill-posedness of the system under different parameter regimes, with emphasis on the optimal ill-posedness result for the two-dimensional BBM-BBM system.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
Davide Torlo, Mario Ricchiuto
Summary: This article focuses on numerical modeling of water waves using depth averaged models. It considers PDE systems that consist of a nonlinear hyperbolic model and a linear dispersive perturbation involving an elliptic operator. Two strategies are proposed to construct reduced order models for these problems, with emphasis on the control of the overhead related to the inversion of the elliptic operators and the robustness with respect to variations of the flow parameters. The approaches are evaluated on various benchmarks, showing potential for cost reduction and advantages in terms of robustness and cost reduction for different methods.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Hakeem Ullah, Mehreen Fiza, Ilyas Khan, Nawa Alshammari, Nawaf N. Hamadneh, Saeed Islam
Summary: In this study, a new modification of the semi-analytical method, called the fractional optimal auxiliary function method (FOAFM), is used to solve fractional-order KdVs equations. The FOAFM provides a simplified and applicable approach with less computational work and fast convergence. Numerical and graphical results confirm the effectiveness and accuracy of the method.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Junfeng Lu, Yi Sun
Summary: This paper presents two numerical approaches for finding the approximated solutions of the time fractional Boussinesq-Burgers equations with He's fractional derivative. The FCT-HPM and HPTM solutions are provided without any linearization or complicated computation, and numerical comparisons illustrate the efficiency of these methods.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics, Applied
M. M. Khader, Khaled M. Saad, Zakia Hammouch, Dumitru Baleanu
Summary: This paper investigates the spectral collocation method with the use of Chebyshev polynomials in analyzing space fractional Korteweg-de Vries and space fractional Korteweg-de Vries-Burgers equations based on the Caputo-Fabrizio fractional derivative. The proposed method simplifies the models to ordinary differential equations and solves them effectively, which is the first work studying Caputo-Fabrizio space fractional derivative for the proposed equations. The results are accurate and the method can be applied to various fractional systems.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics
Ahmed B. Khoshaim, Muhammad Naeem, Ali Akgul, Nejib Ghanmi, Shamsullah Zaland
Summary: In this study, the rho-homotopy perturbation transformation method was applied to analyze fifth-order nonlinear fractional KdV equations, demonstrating its validity and efficiency, as well as showing that the solutions for fractional and integer orders converge to the exact results. The technique was successfully utilized for various engineering and science models, proving to be accurate and easy to use.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Asif Khan, Tayyaba Akram, Arshad Khan, Shabir Ahmad, Kamsing Nonlaopon
Summary: This manuscript investigates the Korteweg-de Vries-Burgers (KdV-Burgers) partial differential equation (PDE) under nonlocal operators with the Mittag-Leffler kernel and the exponential decay kernel. The existence of the solution is demonstrated using fixed point theorems and a series solution is computed using the modified double Laplace transform. The suggested approach is verified through comparisons with exact values and the results are further analyzed through graphs and numerical data to compare the two fractional operators.
Article
Mathematics, Applied
Laique Zada, Imran Aziz
Summary: Haar wavelet collocation technique is used to obtain approximate solutions for fractional KdV, Burgers', and KdV-Burgers' equations, involving discretization and solving of nonlinear fractional differential equations. The proposed method demonstrates accuracy, efficiency, and simplicity in many test problems.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Ved Prakash Dubey, Jagdev Singh, Ahmed M. Alshehri, Sarvesh Dubey, Devendra Kumar
Summary: This paper introduces a computational algorithm LFNHAM for exploring the solutions of local fractional coupled equations, investigates their uniqueness and convergence, conducts error analysis and numerical simulations, showing the method's validity and reliability.
Article
Mathematics, Interdisciplinary Applications
Nehad Ali Shah, Praveen Agarwal, Jae Dong Chung, Saad Althobaiti, Samy Sayed, A. F. Aljohani, Mohamed Alkafafy
Summary: In this paper, the q-homotopy analysis transform technique is utilized to analyze the solutions of fractional-order Burgers and diffusion equations, demonstrating its reliability and simplicity. The results are carefully analyzed and several examples are presented to highlight the significance of this work. The proposed method proves to be successful in investigating other fractional-order linear and nonlinear partial differential equations.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Thermodynamics
Mingshuo Liu, Lijun Zhang, Yong Fang, Huanhe Dong
Summary: This study explores the advantages of fractional derivative models over integer order models for fluids between elastic and viscous materials. Using the bilinear method, solutions to the time fractional Burgers equation and Boussinesq-Burgers equations for different fractional orders were derived, revealing properties such as time memory and increased oscillation frequency with higher fractional orders. The results suggest that fractional derivatives can enhance control performance in complex systems with fluids between different elastic and viscous materials.
Article
Mathematics, Applied
Zhi-An Wang, Anita Yang, Kun Zhao
Summary: This paper investigates the existence and stability of traveling wave solutions of the Boussinesq-Burgers system, which describes the propagation of bores. By assuming weak dispersion of the fluid, we establish the existence of three different wave profiles using geometric singular perturbation theory and phase plane analysis. Furthermore, we prove the nonlinear asymptotic stability of the traveling wave solutions against small perturbations using the method of weighted energy estimates. Numerical simulations are conducted to showcase the generation and propagation of various wave profiles in both weak and strong dispersions, confirming our analytical results and showing that the Boussinesq-Burgers system can generate numerous propagating wave profiles depending on the profiles of initial data and the intensity of fluid dispersion.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Mathematics, Interdisciplinary Applications
Rachana Shokhanda, Pranay Goswami, Ji-Huan He, Ali Althobaiti
Summary: In this paper, the time-fractional two-mode coupled Burgers equation with the Caputo fractional derivative is considered, and the He-Laplace method is applied to find its approximate analytical solution. The method decomposes the equation into a series of linear equations, which can be easily solved through Laplace transform. The step-by-step illustration of the solution process demonstrates the method's effectiveness for fractional differential equations.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Hussam Aljarrah, Mohammad Alaroud, Anuar Ishak, Maslina Darus
Summary: This article utilizes the Laplace residual power series approach to study nonlinear systems of time-fractional partial differential equations with time-fractional Caputo derivative. The proposed technique is based on a new fractional expansion of the Maclurian series, providing rapid convergence series solutions for various physical applications. The results obtained are reliable, efficient, and accurate.
FRACTAL AND FRACTIONAL
(2022)
Article
Engineering, Multidisciplinary
Emad A-B Abdel-Salam, Mohamed S. Jazmati, Hijaz Ahmad
Summary: This paper presents a systematic formulation of a new family of Burgers-like equations with fractional space-time order, constructing exact solutions using the direct method. A geometrical study for the fractional space is applied to the obtained solutions, revealing that the arbitrariness of fraction orders makes systems even richer.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Applied
Behzad Nemati Saray, Mehrdad Lakestani, Mehdi Dehghan
Summary: The paper presents the design, analysis, and testing of the multiwavelets Galerkin method for solving the two-dimensional Burgers equation. By discretizing time using the Crank-Nicolson scheme, a PDE is obtained for each time step and then solved using the multiwavelets Galerkin method. The results demonstrate the effectiveness of the method by reducing the number of nonzero coefficients while maintaining the error within a certain range.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Majid Haghi, Mohammad Ilati, Mehdi Dehghan
Summary: In this paper, a high-order compact scheme is proposed for solving two-dimensional nonlinear time-fractional fourth-order reaction-diffusion equations. The unique solvability of the numerical method is proved in detail, and the convergence of the proposed algorithm is proved using the energy method. Numerical examples are given to verify the theoretical analysis and efficiency of the developed scheme.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mathematics, Applied
Hadi Mohammadi-Firouzjaei, Hojatollah Adibi, Mehdi Dehghan
Summary: In this paper, backward difference and local discontinuous Galerkin (BDLDG) methods are used for temporal and spatial discretization of fourth-order partial integrodifferential equations (PIDEs) with memory terms containing weakly singular kernels. The stability analysis of the proposed method is provided, and numerical experiments demonstrate the stability of the resulting scheme and numerically show that the optimal convergence rate is O(h(k+1)) in the discrete L(2)norm.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Mohammad Shirzadi, Mohammadreza Rostami, Mehdi Dehghan, Xiaolin Li
Summary: In this paper, a valuation algorithm is developed for pricing American options under the regime-switching jump-diffusion processes, using a combination of moving least-squares approximation and an operator splitting method. The numerical experiments with American options under different regimes demonstrate the efficiency and effectiveness of the proposed computational scheme.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Green & Sustainable Science & Technology
Abbas Akbari Jouchi, Abolfazl Pourrajabian, Saeed Rahgozar, Maziar Dehghan
Summary: This study quantitatively investigates the negative impact of inappropriate rotor hub configuration on the performance of small wind turbine blades. It shows that coupling the hub configuration with the blade design is essential for small rotor design. The structural analysis of the proposed hub configurations also confirms their suitability.
CLEAN TECHNOLOGIES AND ENVIRONMENTAL POLICY
(2023)
Article
Engineering, Multidisciplinary
Mostafa Abbaszadeh, Ali Ebrahimijahan, Mehdi Dehghan
Summary: This article presents a numerical technique based on the compact local integrated radial basis function (CLI-RBF) method for solving ill-posed inverse heat problems (IHP) with continuous/discontinuous heat source. The space derivative is discretized using the CLIRBF procedure, resulting in a system of ODEs related to the time variable. The final system of ODEs is solved using an adaptive fourth-order Runge-Kutta algorithm. The new numerical method is verified through challenging examples and found to be accurate for solving IHP with continuous/discontinuous heat source in one-and two-dimensional cases.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Materials Science, Multidisciplinary
Yongyi Gu, Syed Maqsood Zia, Mubeen Isam, Jalil Manafian, Afandiyeva Hajar, Mostafa Abotaleb
Summary: In this article, the generalized (2+1)-dimensional shallow water wave equation, which allows unidirectional propagation of shallow-water waves, is investigated. By exploiting the integrability of the system, various forms of solitary wave solutions are obtained using the rogue wave and semi-inverse variational principle (SIVP) schemes. Specifically, four solutions including rogue wave, soliton, bright soliton, dark soliton, and lump solutions are studied. An illustrative example of the Helmholtz equation is provided to demonstrate the feasibility and reliability of the used procedure in this study. The impact of free parameters on the behavior of the obtained solutions is also analyzed, considering the nonlinear nature of the system. The dynamic properties of the obtained results are visualized and analyzed using density, two-dimensional, and three-dimensional images, and the physical nature of the solutions is presented.
RESULTS IN PHYSICS
(2023)
Article
Psychology, Multidisciplinary
Zahra Pourbehbahani, Esmaeel Saemi, Ming-Yang Cheng, Mohammad Reza Dehghan
Summary: Neurofeedback and self-controlled practice are effective techniques for improving motor learning and performance. The study found that SMR neurofeedback and self-controlled practice independently facilitated golf putting in novice golfers, and the positive effects of neurofeedback practice were maintained in the follow-up test. Participation in neurofeedback practice also enhanced the power of the SMR wave, regardless of the type of self-controlled practice used.
BEHAVIORAL SCIENCES
(2023)
Article
Mathematics, Applied
Mostafa Abbaszadeh, Mahmoud A. Zaky, Ahmed S. Hendy, Mehdi Dehghan
Summary: In this paper, a numerical formulation with second-order accuracy in the time direction and spectral accuracy in the space variable is proposed for solving a nonlinear high-dimensional Rosenau-Burgers equation. The spectral element method and the two-grid idea are combined to simulate the equation, and a three-level algorithm is used for the proposed technique. The existence and uniqueness of the solutions to Steps 1, 2, and 3 are investigated, and error analysis is also discussed.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Mehdi Dehghan, Zeinab Gharibi, Ricardo Ruiz-Baier
Summary: In this article, a fully coupled, nonlinear, and energy-stable virtual element method (VEM) is proposed and analyzed for solving the coupled Poisson-Nernst-Planck (PNP) and Navier-Stokes (NS) equations. The stability, existence, and uniqueness of solution of the associated VEM are proved, and optimal error estimates for both the electrostatic potential and ionic concentrations of PNP equations, as well as for the velocity and pressure of NS equations, are derived. Numerical experiments are presented to support the theoretical analysis and demonstrate the method's performance in simulating electrokinetic instabilities in ionic fluids and studying their dependence on ion concentration and applied voltage.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Rooholah Abedian, Mehdi Dehghan
Summary: This paper presents a new formulation of conservative finite difference radial basis function weighted essentially non-oscillatory (WENO-RBF) schemes to solve conservation laws. Unlike previous methods, the flux function is generated directly with the conservative variables, and arbitrary monotone fluxes can be employed. Numerical simulations of several benchmark problems are conducted to demonstrate the good performance of the new scheme.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Fatemeh Asadi-Mehregan, Pouria Assari, Mehdi Dehghan
Summary: This paper presents a computational algorithm for solving nonlinear systems of ordinary and partial differential equations resulting from HIV infection models. The method uses local radial basis functions as shape functions in the discrete collocation scheme, approximating the solution by a small set of nodes. The computational efficiency of the scheme is studied through several test examples.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Construction & Building Technology
Hamed Bagheri-Esfeh, Mohammad Reza Dehghan
Summary: This paper proposes an innovative method to design and optimize a suitable solar combisystem for a residential building. Multiple configurations of solar combisystems are evaluated and the best design is chosen using advanced algorithms. The results show that the total solar fraction of the system is improved by 7.3%.
JOURNAL OF BUILDING ENGINEERING
(2023)
Article
Mathematics
Wensheng Chen, Jalil Manafian, Khaled Hussein Mahmoud, Abdullah Saad Alsubaie, Abdullah Aldurayhim, Alabed Alkader
Summary: This paper studies the Gilson-Pickering (GP) equation and its applications in plasma physics and crystal lattice theory. The model is explained, and various solutions are obtained using different techniques. The superiority and novelty of the new mathematical theory are demonstrated through theorems and examples.
