Results 171 to 180 of about 1,124 (201)
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A class of nonstandard finite difference methods for the Burgers–Huxley equation
Journal of Difference Equations and Applications, 2021In this work, a class of nonstandard finite difference (NSFD) methods is proposed to approximate the exact solution of a diffusive partial differential equation with Burgers convection effect and H...
W. D. Qin +3 more
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Divergence Properties of the Nonstandard Finite Difference Methods
IEEE Microwave and Wireless Components Letters, 2007Yee's classic algorithm was proved to be divergence-free in source-free regions. However, the divergence properties of the nonstandard finite difference (NSFD) methods have not been addressed. In this letter, we investigate the divergence nature of the NSFD (2,2) and (2,4) algorithms.
Bo Yang, Constantine A. Balanis
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Contributions to the mathematics of the nonstandard finite difference method and applications
Numerical Methods for Partial Differential Equations, 2001AbstractWe formalize the transfer of essential properties of the solution of a differential equation to the solution of a discrete scheme as qualitative stability with respect to the properties. This permits us to motivate some rules (viz. on the order of the difference equation, on the renormalization of the denominator of the discrete derivative, and
Anguelov, Roumen, Lubuma, Jean M.-S.
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On the use of nonstandard finite difference methods†
Journal of Difference Equations and Applications, 2005Many real life problems are modelled by differential equations, for which analytical solutions are not always easy to find. One of the most difficult problems is how to solve these differential equations efficiently. Several researchers have tried to do this in various different ways (e.g. via Finite Element Methods, Standard Finite Difference Methods,
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Numerical Dynamics of Nonstandard Finite Difference Method for Nonlinear Delay Differential Equation
International Journal of Bifurcation and Chaos, 2018In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered,
Xiaolan Zhuang +2 more
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Nonstandard finite-difference methods for predator–prey models with general functional response
Mathematics and Computers in Simulation, 2008The authors propose a class of nonstandard finite difference methods for the numerical approximation of the solutions of certain predator-prey systems. The emphasis of the paper is on the qualitative analysis of the methods, including a thorough investigation of properties asserting that the numerical solution reproduces the most important analytical ...
Dobromir T. Dimitrov +1 more
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IEEE Transactions on Magnetics, 2011
Optimal coefficients of the spatial finite difference (FD) operator for the complex nonstandard finite difference time-domain (CNS-FDTD) method are presented. To derive the optimal coefficients that minimize the dispersion error, we employ a semianalytical method based on the FD Laplacian.
Tadao Ohtani, Yasushi Kanai
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Optimal coefficients of the spatial finite difference (FD) operator for the complex nonstandard finite difference time-domain (CNS-FDTD) method are presented. To derive the optimal coefficients that minimize the dispersion error, we employ a semianalytical method based on the FD Laplacian.
Tadao Ohtani, Yasushi Kanai
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Numerical Methods for Partial Differential Equations, 2020
AbstractIn this work, we construct four versions of nonstandard finite difference schemes in order to solve the FitzHugh–Nagumo equation with specified initial and boundary conditions under three different regimes giving rise to three cases. The properties of the methods such as positivity and boundedness are studied. The numerical experiment chosen is
Koffi M. Agbavon, Appanah Rao Appadu
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AbstractIn this work, we construct four versions of nonstandard finite difference schemes in order to solve the FitzHugh–Nagumo equation with specified initial and boundary conditions under three different regimes giving rise to three cases. The properties of the methods such as positivity and boundedness are studied. The numerical experiment chosen is
Koffi M. Agbavon, Appanah Rao Appadu
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Analysis of a mathematical model for cancer treatment by the nonstandard finite difference methods
Journal of Difference Equations and Applications, 2017AbstractWe construct two nonstandard finite difference schemes and use them to study a mathematical model of cancer therapy. Several recent studies show various aspects of the immune response against the cancer. Our discrete models emphasize the role of antibodies in any form of therapy by taking into account the development of anticancer therapies ...
Marc E. Songolo, Issa Ramadhani
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The Nonstandard Finite Difference Method Applied to Pharmacokinetic Models
2018A thesis submitted in fullment of the requirements for the degree of Doctor of Philosophy in the School of Computer Science and Applied Mathematics , University of the Witwatersrand, Johannesburg, July 2018 ; A good understanding of pharmacokinetic-pharmacodynamic can shed light on situations where one or the other needs to be optimized in drug ...
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