Article
Materials Science, Multidisciplinary
Hijaz Ahmad, Tufail A. Khan, Predrag S. Stanimirovic, Wasfi Shatanawi, Thongchai Botmart
Summary: This study investigates the modified variational iteration algorithm-I, which is used for solving different types of nonlinear partial differential equations in modeling physical phenomena. The algorithm incorporates a supplementary parameter to ensure faster convergence. The results obtained from this algorithm are compared with exact and numerical solutions produced by various methods, demonstrating its efficiency, precision, and applicability. The proposed algorithm is highly valuable for solving practical problems in fields of applied physical sciences and engineering.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Aisha Abdullah Alderremy, Rasool Shah, Nehad Ali Shah, Shaban Aly, Kamsing Nonlaopon
Summary: The aim of this article is to compare two analytical approaches, namely the new approximate analytical approach (NAAA) and Mohand variational iteration transform approach (MVITA), for obtaining the solution of the time-fractional system of partial differential equations. Both approaches provide series form solutions and were compared for the proposed problems. The obtained results demonstrate the validity and applicability of the proposed algorithms, which can be extended to analyze other physical phenomena in science and technology.
Article
Mathematics, Applied
Ming-Hui Ding, Guang-Hui Zheng
Summary: This study proposes a method for the inverse reaction coefficient problem of a time-dependent nonlocal diffusion equation by utilizing nonlocal flux measurement and variational regularization method, which can accurately estimate the solution and quantify the uncertainty of the solution.
Review
Engineering, Mechanical
Vahid Reza Hosseini, Wennan Zou
Summary: This paper investigates the numerical solution of time-fractional convection diffusion equations (TF-CDEs), and develops a nonlocal model using the Peridynamic differential operator for discretization. The proposed scheme is analyzed for stability and error estimates, and numerical experiments are conducted to validate the theoretical analysis and demonstrate computational efficiency.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Jonas Berx, Joseph O. Indekeu
Summary: An iteration sequence based on the BLUES function method is proposed for calculating analytic approximants to solutions of nonlinear partial differential equations. The method is tested on multiple examples and proven to be a worthwhile alternative option.
PHYSICAL REVIEW RESEARCH
(2021)
Article
Physics, Multidisciplinary
Costantino Di Bello, Aleksei Chechkin, Alexander K. Hartmann, Zbigniew Palmowski, Ralf Metzler
Summary: Stochastic resetting is a rapidly developing topic that studies the occasional reset of a diffusing particle to its starting point and its effects on optimal first-passage times to a target. The concept of partial resetting has been established and analyzed, and here we further develop a technique to determine the time-dependent probability density function (PDF) for Markov processes with partial resetting. We obtain an exact representation of the PDF for general symmetric Lévy flights with stable index 0 < a ≤ 2, and for Cauchy and Brownian motions (a = 1, 2), the PDF can be expressed in terms of elementary functions in position space. We also determine the stationary PDF and observe intricate crossover behaviors as a function of time in our numerical analysis.
NEW JOURNAL OF PHYSICS
(2023)
Article
Mathematics, Applied
Renu Choudhary, Satpal Singh, Devendra Kumar
Summary: This paper proposes a numerical scheme for a class of time-fractional convection-reaction-diffusion problems with a time lag, and verifies the effectiveness of the proposed numerical scheme through stability and convergence analysis.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Physics, Multidisciplinary
Jiaohui Xu, Tomas Caraballo
Summary: This paper studies the asymptotic behavior of solutions to nonlocal stochastic partial differential equations with multiplicative and additive noise; the existence of random attractors is established by transforming and constructing dynamical systems; in the case of zero external forcing term, the random attractor becomes a singleton.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Operations Research & Management Science
Annamaria Barbagallo, Serena Guarino Lo Bianco
Summary: The paper discusses the problem of random time-dependent oligopolistic market equilibrium and studies it from the policymaker's point of view. The conditions for random dynamic optimal control equilibrium are expressed through an inverse stochastic time-dependent variational inequality, which is shown to be equivalent to a stochastic time-dependent variational inequality. The paper obtains some results regarding the existence and well-posedness of optimal regulatory taxes, and presents a numerical scheme for computing the solution to the stochastic time-dependent variational inequality. An example is also discussed.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2023)
Article
Mathematics, Applied
R. Faizi, R. Atmania
Summary: In this paper, we investigate an inverse problem of determining the time-dependent source coefficient in a semilinear reaction-diffusion equation. We prove the existence and uniqueness of the classical solution by Fourier analysis and the iteration method, and show the continuous dependence of this solution upon the additional data of the inverse problem.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics, Applied
Yong Zhi Zhao, Zhi Yong Ai
Summary: This paper proposes a general framework of the transformed differential quadrature method (TDQM) for solving partial differential equations (PDEs). The TDQM introduces the integral transform theorem to decompose the solution process, reducing the difficulty of large-scale matrix inversion and improving computational efficiency. It also reduces the limitation and influence of boundary conditions on computational results, making it suitable for multi-dimensional problems with complex variables.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Vitaly Kalinin, Alexander Shlapunov, Konstantin Ushenin
Summary: This study considers a mathematical model that relates to reconstructing cardiac electrical activity from ECG measurements on the body surface. By applying recent developments in solving boundary value problems for elliptic and parabolic equations in Sobolev type spaces, uniqueness theorems for the model have been obtained. These results can serve as a sound foundation for creating numerical methods for non-invasive mapping of the heart.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Mathematics, Applied
Ibrahim Tekin
Summary: This article studies the inverse problem of recovering a time-dependent coefficient of a nonlinear third order PDE from knowledge of a one boundary measurement.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Yu-Ming Chu, Ehab Hussein Bani Hani, Essam R. El-Zahar, Abdelhalim Ebaid, Nehad Ali Shah
Summary: The article investigated fractional third-order dispersive partial differential equations using Shehu decomposition and variational iteration transform methods. Various fractional-order integral, derivative, and function were used as the basis of the methodology, with graphs and tables showing solution behavior. The comparison demonstrated the signed agreement of solutions and their accuracy, efficiency, and reliability were confirmed through numerical experiments.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Nehad Ali Shah, S. Saleem, Ali Akgul, Kamsing Nonlaopon, Jae Dong Chung
Summary: This paper introduces a new semi-analytical technique called the variational iteration transform method for solving fractional-order diffusion equations, and verifies the validity of the proposed method and its higher accuracy through numerical problems. The method also simplifies the calculation of the multiplier using the Shehu transformation, providing value to researchers dealing with various linear and nonlinear problems.
JOURNAL OF FUNCTION SPACES
(2021)
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
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, Mohammad Ivan Azis, Mehdi Dehghan, Reza Mohammadi-Arani
Summary: This paper proposes a new meshless numerical procedure, namely the gradient smoothing method (GSM), for simulating the pollutant transition equation in urban street canyons. The time derivative is approximated using the finite difference scheme, while the space derivative is discretized using the gradient smoothing method. Additionally, the proper orthogonal decomposition (POD) approach is employed to reduce CPU time. Several real-world examples are solved to verify the efficiency of the developed numerical procedure.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Biology
Niusha Narimani, Mehdi Dehghan
Summary: This paper numerically studies the therapies of prostate cancer in a two-dimensional space. The proposed model describes the tumor growth driven by a nutrient and the effects of cytotoxic chemotherapy and antiangiogenic therapy. The results obtained without using any adaptive algorithm show the response of the prostate tumor growth to different therapies.
COMPUTERS IN BIOLOGY AND MEDICINE
(2023)
Article
Engineering, Multidisciplinary
Mostafa Abbaszadeh, Yasmin Kalhor, Mehdi Dehghan, Marco Donatelli
Summary: The purpose of this research is to develop a numerical method for option pricing in jump-diffusion models. The proposed model consists of a backward partial integro-differential equation with diffusion and advection factors. Pseudo-spectral technique and cubic B-spline functions are used to solve the equation, and a second-order Strong Stability Preserved Runge-Kutta procedure is adopted. The efficiency and accuracy of the proposed method are demonstrated through various test cases.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Mahboubeh Najafi, Mehdi Dehghan
Summary: In this work, two-dimensional dendritic solidification is simulated using the meshless Diffuse Approximate Method (DAM). The Stefan problem is studied through the phase-field model, considering both isotropic and anisotropic materials for comparisons. The effects of changing some constants on the obtained patterns are investigated.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Computer Science, Interdisciplinary Applications
Hasan Zamani-Gharaghoshi, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: This paper presents a local meshless collocation method for solving reaction-diffusion systems on surfaces. The proposed numerical procedure utilizes Pascal polynomial approximation and closest point method. This method is geometrically flexible and can be used to solve partial differential equations on unstructured point clouds. It only requires a set of arbitrarily scattered mesh-free points representing the underlying surface.
ENGINEERING WITH COMPUTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Reza MohammadiArani, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: Different coupled systems for the shallow water equation, bed elevation, and suspended load equation have been proposed. The main goal of this paper is to utilize an advanced lattice Boltzmann method (LBM) to solve this system of equations. In addition, a practical approach is developed for applying open boundary conditions in order to relax the solution onto a prescribed equilibrium flow.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mathematics, Applied
Mehdi Dehghan, Zeinab Gharibi
Summary: This paper discusses the incompressible miscible displacement of two-dimensional Darcy-Forchheimer flow and formulates a mathematical model with two partial differential equations: a Darcy-Forchheimer flow equation for the pressure and a convection-diffusion equation for the concentration. The model is discretized using a fully mixed virtual element method (VEM) and stability, existence, and uniqueness of the associated mixed VEM solution are proved under smallness data assumption. Optimal error estimates are obtained for concentration, auxiliary flux variables, and velocity, and several numerical experiments are presented to support the theoretical analysis and illustrate the applicability for solving actual problems.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Fatemeh Asadi-Mehregan, Pouria Assari, Mehdi Dehghan
Summary: In this research, we present a numerical approach for solving a specific type of nonlinear integro-differential equations derived from Volterra's population model. This model captures the growth of a biological species in a closed system and includes an integral term to account for toxin accumulation. The proposed technique utilizes the discrete Galerkin scheme with the moving least squares (MLS) algorithm to estimate the solution of the integro-differential equations.
INTERNATIONAL JOURNAL OF COMPUTER 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
Alireza Hosseinian, Pouria Assari, Mehdi Dehghan
Summary: This paper presents a numerical method for solving nonlinear Volterra integral equations with delay arguments. The method uses the discrete collocation approach with thin plate splines as a type of radial basis functions. The method provides an effective and stable algorithm to estimate the solution, which can be easily implemented on a personal computer. The error analysis and convergence validation of the method are also provided.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Engineering, Multidisciplinary
Ali Ebrahimijahan, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: In this study, the integrated radial basis functions-partition of unity (IRBF-PU) method is proposed for solving the coupled Schrodinger-Boussinesq equations in one-and two-dimensions. The IRBF-PU method is a local mesh-free method that offers flexibility and high accuracy for PDEs with smooth initial conditions. Numerical simulations demonstrate that the IRBF-PU method can effectively simulate solitary waves and preserve conservation laws. Furthermore, the obtained results are compared with other methods in the literature to validate the effectiveness and reliability of the proposed method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Hasan Zamani-Gharaghoshi, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: This article presents a numerical method for solving the surface Allen-Cahn model. The method is based on the generalized moving least-squares approximation and the closest point method. It does not depend on the structure of the underlying surface and only requires a set of arbitrarily distributed mesh-free points on the surface.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics, Applied
M. S. Bruzon, T. M. Garrido, R. de la Rosa
Summary: We study a family of generalized Zakharov-Kuznetsov modified equal width equations in (2+1)-dimensions involving an arbitrary function and three parameters. By using the Lie group theory, we classify the Lie point symmetries of these equations and obtain exact solutions. We also show that this family of equations admits local low-order multipliers and derive all local low-order conservation laws through the multiplier approach.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Dohee Jung, Changbum Chun
Summary: The paper presents a general approach to enhance the Pade iterations for computing the matrix sign function by selecting an arbitrary three-point family of methods based on weight functions. The approach leads to a multi-parameter family of iterations and allows for the discovery of new methods. Convergence and stability analysis as well as numerical experiments confirm the improved performance of the new methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Abhishek Yadav, Amit Setia, M. Thamban Nair
Summary: In this paper, we propose a Galerkin's residual-based numerical scheme for solving a system of Cauchy-type singular integral equations using Chebyshev polynomials. We prove the well-posedness of the system and derive a theoretical error bound and convergence order. The numerical examples validate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fernando Chacon-Gomez, M. Eugenia Cornejo, Jesus Medina, Eloisa Ramirez-Poussa
Summary: The use of decision rules allows for reliable extraction of information and inference of conclusions from relational databases, but the concepts of decision algorithms need to be extended in fuzzy environments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Ilhame Amirali, Gabil M. Amiraliyev
Summary: This paper considers the one-dimensional initial-boundary problem for a pseudoparabolic equation with a time delay. To solve this problem numerically, a higher-order difference method is constructed and the error estimate for its solution is obtained. Based on the method of energy estimates, the fully discrete scheme is shown to be convergent of order four in space and of order two in time. The given numerical results illustrate the convergence and effectiveness of the numerical method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Tong-tong Shang, Guo-ji Tang, Wen-sheng Jia
Summary: The goal of this paper is to investigate a class of linear complementarity problems over tensor-spaces, denoted by TLCP, which is an extension of the classical linear complementarity problem. First, two classes of structured tensors over tensor-spaces (i.e., T-R tensor and T-RO tensor) are introduced and some equivalent characterizations are discussed. Then, the lower bound and upper bound of the solutions in the sense of the infinity norm of the TLCP are obtained when the problem has a solution.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Fabio Difonzo, Pawel Przybylowicz, Yue Wu
Summary: This paper focuses on the existence, uniqueness, and approximation of solutions of delay differential equations (DDEs) with Caratheodory type right-hand side functions. It presents the construction of the randomized Euler scheme for DDEs and investigates its error. Furthermore, the paper reports the results of numerical experiments.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Priyanka Roy, Geetanjali Panda, Dong Qiu
Summary: In this article, a gradient based descent line search scheme is proposed for solving interval optimization problems under generalized Hukuhara differentiability. The innovation and importance of these concepts are presented from practical and computational perspectives. The necessary condition for existence of critical point is presented in inclusion form of interval-valued gradient. Suitable efficient descent direction is chosen based on the monotonic property of the interval-valued function and specific interval ordering. Mathematical convergence of the scheme is proved under the assumption of Inexact line search. The theoretical developments are implemented with a set of interval test problems in different dimensions. A possible application in finance is provided and solved by the proposed scheme.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Zhongqian Wang, Changqing Ye, Eric T. Chung
Summary: In this paper, the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions for elasticity equations in high contrast media is developed. The method offers advantages such as independence of target region's contrast from precision and significant impact of oversampling domain sizes on numerical accuracy. Furthermore, this is the first proof of convergence of CEM-GMsFEM with mixed boundary conditions for elasticity equations. Numerical experiments demonstrate the method's performance.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Samaneh Soradi-Zeid, Maryam Alipour
Summary: The Laguerre polynomials are a new set of basic functions used to solve a specific class of optimal control problems specified by integro-differential equations, namely IOCP. The corresponding operational matrices of derivatives are calculated to extend the solution of the problem in terms of Laguerre polynomials. By considering the basis functions and using the collocation method, the IOCP is simplified into solving a system of nonlinear algebraic equations. The proposed method has been proven to have an error bound and convergence analysis for the approximate optimal value of the performance index. Finally, examples are provided to demonstrate the validity and applicability of this technique.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Almudena P. Marquez, Maria L. Gandarias, Stephen C. Anco
Summary: A generalization of the KP equation involving higher-order dispersion is studied. The Lie point symmetries and conservation laws of the equation are obtained using Noether's theorem and the introduction of a potential. Sech-type line wave solutions are found and their features, including dark solitary waves on varying backgrounds, are discussed.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Susanne Saminger-Platz, Anna Kolesarova, Adam Seliga, Radko Mesiar, Erich Peter Klement
Summary: In this article, we study real functions defined on the unit square satisfying basic properties and explore the conditions for generating bivariate copulas using parameterized transformations and other constructions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Lulu Tian, Nattaporn Chuenjarern, Hui Guo, Yang Yang
Summary: In this paper, a new local discontinuous Galerkin (LDG) algorithm is proposed to solve the incompressible Euler equation in two dimensions on overlapping meshes. The algorithm solves the vorticity, velocity field, and potential function on different meshes. The method employs overlapping meshes to ensure continuity of velocity along the interfaces of the primitive meshes, allowing for the application of upwind fluxes. The article introduces two sufficient conditions to maintain the maximum principle of vorticity.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Cheng Wang, Jilu Wang, Steven M. Wise, Zeyu Xia, Liwei Xu
Summary: In this paper, a temporally second-order accurate numerical scheme for the Cahn-Hilliard-Magnetohydrodynamics system of equations is proposed and analyzed. The scheme utilizes a modified Crank-Nicolson-type approximation for time discretization and a mixed finite element method for spatial discretization. The modified Crank-Nicolson approximation allows for mass conservation and energy stability analysis. Error estimates are derived for the phase field, velocity, and magnetic fields, and numerical examples are presented to validate the proposed scheme's theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Mingyu He, Wenyuan Liao
Summary: This paper presents a numerical method for solving reaction-diffusion equations in spatially heterogeneous domains, which are commonly used to model biological applications. The method utilizes a fourth-order compact alternative directional implicit scheme based on Pade approximation-based operator splitting techniques. Stability analysis shows that the method is unconditionally stable, and numerical examples demonstrate its high efficiency and high order accuracy in both space and time.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
