Results 141 to 150 of about 928 (167)
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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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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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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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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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SIAM Journal on Scientific Computing, 2001
Summary: The relationship between the so-called nonstandard finite-difference schemes and the nodal integral method (NIM) is investigated using the Fisher equation as a model problem. Exact and best finite-difference schemes are reviewed first. Next, the NIM for the Fisher equation is developed.
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Summary: The relationship between the so-called nonstandard finite-difference schemes and the nodal integral method (NIM) is investigated using the Fisher equation as a model problem. Exact and best finite-difference schemes are reviewed first. Next, the NIM for the Fisher equation is developed.
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Nonstandard finite difference methods: recent trends and further developments
Journal of Difference Equations and Applications, 2016In this paper, we review many recent developments and further applications of nonstandard finite difference (NSFD) methods encountered in the past decade. In particular, it is a follow up article of the one published in 2005 [K.C. Patidar, On the use of non-standard finite difference methods, J. Differ. Equ. Appl. 11 (2005), pp. 735–758].
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A nonstandard finite difference numerical method for an oscillatory diffusion-reaction problem
2021Discretization schemes based on NonStandard Finite Differences (NSFD) are a modification of Standard Finite Differences (SFD) schemes in which the classical denominators are usually replaced by particular denominator functions that satisfy certain conditions.
Conte Dajana +2 more
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