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Articles 1 - 12 of 12
Full-Text Articles in Numerical Analysis and Computation
(R2167) Global Stability Of Seirs Model With Single Dose Vaccination In Varying Population, Govind Jha, Prabhat Mandal, Sarita Jha
(R2167) Global Stability Of Seirs Model With Single Dose Vaccination In Varying Population, Govind Jha, Prabhat Mandal, Sarita Jha
Applications and Applied Mathematics: An International Journal (AAM)
Understanding the evolution of infectious diseases within a dynamic population is essential for formulating effective public health strategies. This work introduces an enhanced SEIRS epidemic model that incorporates demographic variation and a single-dose vaccination strategy, supporting that immunity can be reduced over time. The model reflects diseases in which individuals may return to the susceptible state after recovery. Extending prior reduced three-dimensional models, this study develops a complete four-dimensional SEIRS framework, thereby increasing the model’s applicability to real-world scenarios. The inclusion of the full system presents greater analytical challenges. To overcome this, we extend the second additive compound matrix and …
Qualitative Analysis Of Solutions To A General Class Of Nonlinear Difference Equations With Applications, Osama Moaaz, Mohamed F. Abouelenein, Mona Anis
Qualitative Analysis Of Solutions To A General Class Of Nonlinear Difference Equations With Applications, Osama Moaaz, Mohamed F. Abouelenein, Mona Anis
Mathematical Modelling and Numerical Simulation with Applications
This work examines the qualitative behavior of a general class of difference equations. We establish criteria guaranteeing the stability, periodicity, and boundedness of the solutions of the equation under consideration. In addition, we identify its invariant intervals. The theoretical results are subsequently applied to various special cases, among them the May--Host model. Numerical simulations are presented to demonstrate the dynamics of the solutions and to validate the theoretical analysis.
Mathematical Analysis And Numerical Simulation Of A Fractional-Order Sir-Si Model For Malaria Transmission Dynamics, Gassan A. M. O. Farah, Abdulaziz Y. A. Mukhtar, Kailash C. Patidar
Mathematical Analysis And Numerical Simulation Of A Fractional-Order Sir-Si Model For Malaria Transmission Dynamics, Gassan A. M. O. Farah, Abdulaziz Y. A. Mukhtar, Kailash C. Patidar
Mathematical Modelling and Numerical Simulation with Applications
This study investigates the complex transmission dynamics of malaria, a critical global health challenge, with a focus on the African continent. We introduce a novel approach that employs Fractional Differential Equations (FDEs) to advance the understanding of malaria spread and control. Specifically, we develop a new SIR-SI model using the Caputo fractional operator, which captures the memory effects and time-delay characteristics inherent in real-world epidemiological systems. A detailed analysis of the model's solvability and uniqueness is conducted using fixed-point theory. To obtain an analytical solution, the system is solved via the Laplace transform method, with solutions expressed in closed form …
(Si15-068) Advanced Numerical Methods For The Solution Of Nonlinear Fisher Equation, Vikash Vimal, Richa Kumari, Ashish Awasthi
(Si15-068) Advanced Numerical Methods For The Solution Of Nonlinear Fisher Equation, Vikash Vimal, Richa Kumari, Ashish Awasthi
Applications and Applied Mathematics: An International Journal (AAM)
This paper examines the use of advanced numerical techniques to approximate solutions of the Fisher equation with higher-order accuracy. This technique integrates the method of lines with a strong stability-preserving Runge–Kutta scheme of orders four and five stages (SSPRK-54) for the numerical formulation. This scheme is then tested on two examples and the results show that it is more efficient than existing methods and requires less computing power. These equations are widely used across scientific and engineering disciplines, with particular relevance in biomedical studies, such as estimating the boundary size of tumors. The difficulties arising from their nonlinear nature are …
(Si10-056) Fear Effect In A Three Species Prey-Predator Food-Web System With Harvesting, R. P. Gupta, Dinesh K. Yadav
(Si10-056) Fear Effect In A Three Species Prey-Predator Food-Web System With Harvesting, R. P. Gupta, Dinesh K. Yadav
Applications and Applied Mathematics: An International Journal (AAM)
Some recent studies and field experiments show that predators affect their prey not only by direct capture; they also induce fear in prey species, which reduces their reproduction rate. Considering this fact, we propose a mathematical model to study the fear effect of a middle predator on its prey in a three-species food web system with harvesting. The ecological feasibility of solutions to the proposed system is guaranteed in terms of positivity and boundedness. The local stability of stationary points in the proposed system is derived. Multiple co-existing stationary points for the proposed system are observed, which makes the problem …
(R1458) A New Finite Difference Scheme For High-Dimensional Heat Equation, Jafar Biazar, Roxana Asayesh
(R1458) A New Finite Difference Scheme For High-Dimensional Heat Equation, Jafar Biazar, Roxana Asayesh
Applications and Applied Mathematics: An International Journal (AAM)
In this research, a new second-order finite difference scheme is proposed to solve two and three- dimensional heat equation. Finite difference equations are determined via a discretization approach in which spatial second order partial derivatives in x and y directions are approximated simultaneously while in the classic method, each spatial partial derivative is replaced by a central finite difference approximation, separately. By this new discretization scheme and also using the forward difference to the first-order time derivative, a finite difference equation is obtained for the parabolic equation. This approach is explicit and similar to other explicit approaches, an interval for …
Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, Bailey Rester
Stability Analysis Of Krylov Subspace Spectral Methods For The 1-D Wave Equation In Inhomogeneous Media, Bailey Rester
Master's Theses
Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that also possess the stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE. As a result, KSS methods scale effectively to higher spatial resolution. This thesis will present a stability analysis of a first-order KSS method applied to the wave equation in inhomogeneous media.
Modified Gaussian Radial Basis Function Method For The Burgers Systems, Hossein Aminikhah, Mostafa Sadeghi
Modified Gaussian Radial Basis Function Method For The Burgers Systems, Hossein Aminikhah, Mostafa Sadeghi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the systems of variable-coefficient coupled Burgers equation are solved by a free mesh method. The method is based on the collocation points with the modified Gaussian (MGA) radial basis function (RBF). Dependent parameters and independent parameters and their effect on the stability are shown. The accuracy and efficiency of the method has been checked by two examples. The results of numerical experiments are compared with analytical solutions by calculating errors infinity-norm.
Finite Difference Schemes For Variable Order Time-Fractional First Initial Boundary Value Problems, Gunvant A. Birajdar, M. M. Rashidi
Finite Difference Schemes For Variable Order Time-Fractional First Initial Boundary Value Problems, Gunvant A. Birajdar, M. M. Rashidi
Applications and Applied Mathematics: An International Journal (AAM)
The aim of the study is to obtain the numerical solution of first initial boundary value problem (IBVP) for semi-linear variable order fractional diffusion equation by using different finite difference schemes. We developed the three finite difference schemes namely explicit difference scheme, implicit difference scheme and Crank-Nicolson difference scheme, respectively for variable order type semi-linear diffusion equation. For this scheme the stability as well as convergence are studied via Fourier method. At the end, solution of some numerical examples are discussed and represented graphically using Matlab.
A Duhamel Integral Based Approach To Identify An Unknown Radiation Term In A Heat Equation With Non-Linear Boundary Condition, R. Pourgholi, M. Abtahi, A. Saeedi
A Duhamel Integral Based Approach To Identify An Unknown Radiation Term In A Heat Equation With Non-Linear Boundary Condition, R. Pourgholi, M. Abtahi, A. Saeedi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we consider the determination of an unknown radiation term in the nonlinear boundary condition of a linear heat equation from an overspecified condition. First we study the existence and uniqueness of the solution via an auxiliary problem. Then a numerical method consisting of zeroth-, first-, and second-order Tikhonov regularization method to the matrix form of Duhamel's principle for solving the inverse heat conduction problem (IHCP) using temperature data containing significant noise is presented. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method. Some numerical experiments confirm the …
New Computational Algorithms For Analyzing The Stability Of The Differential Equations System, H. S. Najafi, A. H. Refahi Sheikhani
New Computational Algorithms For Analyzing The Stability Of The Differential Equations System, H. S. Najafi, A. H. Refahi Sheikhani
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we show how to improve the approximate solution of the large Lyapunov equation obtained by an arbitrary method. Moreover, we propose a new method based on refinement process and Weighted Arnoldi algorithm for solving large Lyapunov matrix equation. Finally, some numerical results will be reported to illustrate the efficiency of the proposed method.
Some Stability Problems In Droplet Formation And Breakup (Report Lstm 351/T/92)., Nihad E. Daidzic
Some Stability Problems In Droplet Formation And Breakup (Report Lstm 351/T/92)., Nihad E. Daidzic
Aviation Department Publications
In this study the instability of droplets and cylindrical jets is investigated. The understanding of these processes has both academic and practical value. Instability of cylindrical jets is theoretically investigated for infinitesimal and finite, but small initial amplitudes (linear and nonlinear stability). For droplets, only linear theory is presented. It is assumed that the capillary force play a dominant role. It is determined that the viscosity exerts a damping effect. In the first section we give an introduction, after which the linear stability theory of cylindrical liquid jets is presented. In the third section the nonlinear jet stability theory is …