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Articles 1 - 13 of 13
Full-Text Articles in Numerical Analysis and Computation
(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 …
Difference Schemes Of High Accuracy For Equation Of Spin Waves In Magnets, Mirsaid Aripov, Dauletbay Utebaev, Zhusipbay Nurullaev
Difference Schemes Of High Accuracy For Equation Of Spin Waves In Magnets, Mirsaid Aripov, Dauletbay Utebaev, Zhusipbay Nurullaev
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
Three-parameter difference schemes of the finite element method with a high order of accuracy are considered in the article for a mathematical model of spin waves in magnets (Sobolev-type equations). Discretization of time and space variables is conducted on the basis of the finite element method. The parameters of the scheme allow choosing the best approximation and accuracy, and an economic algorithm for numerical implementation. Theorems on the stability and convergence of the considered difference schemes are obtained.
(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 …
Numerical Calculation Of Lyapunov Stable Solutions Of The Hyperbolic Systems, Dilfuza Ne'matova, Aziza Akbarova
Numerical Calculation Of Lyapunov Stable Solutions Of The Hyperbolic Systems, Dilfuza Ne'matova, Aziza Akbarova
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
We give numerical examples demonstrating and confirming the theoretical results obtained for systems of two linear hyperbolic equations.
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.
Using An A Priori Estimate For Constructing Difference Schemes For Quasi-Linear Hyperbolic Systems, Rakhmatillo Aloev, Mirzoali Khudayberganov
Using An A Priori Estimate For Constructing Difference Schemes For Quasi-Linear Hyperbolic Systems, Rakhmatillo Aloev, Mirzoali Khudayberganov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper we consider a class of quasi-linear hyperbolic systems, which allows the construction of a dissipative energy integrals. In the basis of the design and investigation the stability of difference schemes for the numerical solution of the initial boundary value problems for the above class of quasi-linear hyperbolic systems, we put the existence of a discrete analogue of the dissipative energy integrals.
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.
Eigenvalue Methods For Interpolation Bases, Piers W. Lawrence
Eigenvalue Methods For Interpolation Bases, Piers W. Lawrence
Electronic Thesis and Dissertation Repository
This thesis investigates eigenvalue techniques for the location of roots of polynomials expressed in the Lagrange basis. Polynomial approximations to functions arise in almost all areas of computational mathematics, since polynomial expressions can be manipulated in ways that the original function cannot. Polynomials are most often expressed in the monomial basis; however, in many applications polynomials are constructed by interpolating data at a series of
points. The roots of such polynomial interpolants can be found by computing the eigenvalues of a generalized companion matrix pair constructed directly from the values of the interpolant. This affords the opportunity to work with …
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 …
Stability Of A Class Of Discrete Minimum Variance Smoothing Formulas, William F. Trench
Stability Of A Class Of Discrete Minimum Variance Smoothing Formulas, William F. Trench
William F. Trench
No abstract provided.