Last edited by Maugar
Wednesday, July 15, 2020 | History

8 edition of Applications of Nonstandard Finite Difference Schemes found in the catalog.

Applications of Nonstandard Finite Difference Schemes

by Ronald E. Mickens

  • 143 Want to read
  • 11 Currently reading

Published by World Scientific Publishing Company .
Written in English

    Subjects:
  • Applied Mathematics,
  • Calculus & mathematical analysis,
  • Numerical analysis,
  • Science/Mathematics,
  • Finite differences,
  • Mathematical Physics,
  • Mathematics,
  • Numerical solutions,
  • Number Theory,
  • Applied,
  • Applied Sciences,
  • Differential Equations - Partial Differential Equations,
  • Differential equations, Partia,
  • Differential equations, Partial

  • The Physical Object
    FormatHardcover
    Number of Pages250
    ID Numbers
    Open LibraryOL9195091M
    ISBN 10981024133X
    ISBN 109789810241339

    We design nonstandard finite difference (NSFD) schemes which are unconditionally dynamically consistent with respect to the positivity property of solutions of cross-diffusion equations in biosciences. This settles a problem that was open for quite some by: 9. In this section, we describe how a nonstandard finite difference scheme (NSFD) is constructed [15] for the 1D convection-diffusion equation. The equation has three subequations [16] which are given by. Equations (43) and (44) have known exact finite difference scheme which are with and by:

    A multi-step differential transform method and application to non-chaotic or chaotic systems. Computers and Mathematics with Applications, 59(4)–, P. Raja Sekhara Rao, K. Venkata Ratnam, and M. Sita Rama Murthy. Stability preserving non standard finite difference schemes for certain biological : Meksianis Z. Ndii, Nursanti Anggriani, Asep K. Supriatna.   In this paper, we discuss numerical methods for fractional order problems. Some nonstandard finite difference schemes are presented and investigated. The application in the simulation of a fractional-order Brusselator system is hence presented. By means of some numerical experiments, we show the effectiveness of the proposed by:

    Book Description. Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. non-standard finite difference schemes as more reliable numerical the publication ofMickens’s book, the nonstandard finite difference approach wasextensively been applied to differential models originating problems from Engineering, Physics, Biology, Chemistry, etc. In all these contributions of different areas.


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Applications of Nonstandard Finite Difference Schemes by Ronald E. Mickens Download PDF EPUB FB2

The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter 1 gives an overview of the 3/5(1).

This volume provides a concise introduction to the methodology of nonstandard finite difference (NSFD) schemes construction and shows how they can be applied to the numerical integration of differential equations occurring in the natural, biomedical, and engineering by:   Applications of Nonstandard Finite Difference Schemes.

The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to.

An introduction to the methods and philosophy of constructing nonstandard finite difference schemes. It shows how to construct nonstandard schemes and how these are applied to obtain numerical solutions of the differential equations which arise in the study of nonlinear dynamical systems.

In reality, the non-standard finite difference method is an extension of the standard finite difference method. Nonstandard finite difference scheme (NSFD) was introduced as an alternative method for solving numerous problems in mathematical models engage of algebra, biology and differentiation.

Chapter 1 Nonstandard Finite DifFerence Schemes 1 Ronald E. Mickens Introduction 2 Exact Schemes 5 Nonstandard Schemes 19 Applications 23 First-Order Scalar ODE's 23 A Photoconduction Model 26 The Duffing Oscillator 29 Mixed Parity Oscillator 31 A Cubic Reaction Problem in Neurophysiology ().

Nonstandard Finite Difference Schemes for Differential Equations. Journal of Difference Equations and Applications: Vol. 8, No. 9, pp. Cited by: nonstandard finite difference models of differential equations Download nonstandard finite difference models of differential equations or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get nonstandard finite difference models of differential equations book now. This site is like a library, Use search box in the widget to get ebook.

of the consistency between the nonstandard FD model and the original heat transfer problem. The chapter covers a range of topics from unde rgraduate work on standard finite difference solution to ODEs and PDEs through to recent research on nonstandard finite difference schemes for nonlinear heat transfer problems.

Advances in the Applications of Nonstandard Finite Difference Schemes Ronald E. Mickens This volume provides a concise introduction to the methodology of nonstandard finite difference (NSFD) schemes construction and shows how they can be applied to the numerical integration of differential equations occurring in the natural, biomedical, and.

System Upgrade on Tue, May 19th, at 2am (ET) During this period, E-commerce and registration of new users may not be available for up to 12 hours. Provides a concise introduction to the methodology of nonstandard finite difference (NSFD) schemes construction and shows how they can be applied to the numerical integration of differential.

Theory of %onstandard Finite Difference Method The general form of nonstandard method can be written as, y F h y n n+1= (,) (3) Definition 1 (Anguelov and Lubuma, ) A finite difference scheme is called non-standard finite difference method, if at least one of the following conditions is met; i) In the discrete derivative, the traditionalFile Size: KB.

This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary types of numerical instabilities do not occur.

There have been extensive studies and applications of this model. A nonstandard finite difference scheme for the Burgers-Fisher equation was given by Mickens and Gumel [7].

In [8], Kaya and El-Sayed constructed a numerical simulation and explicit solutions of the generalized Burgers-Fisher by: 9. Exact finite difference and non-standard finite difference schemes for. Journal of Difference Equations and Applications: Vol.

18, No. 9, pp. Cited by: Applications of Nonstandard Finite Difference Me thods to Nonlinear Heat Transfer Problems where h is the convection heat transfer coefficient and A is cooloing area. Finite Difference Schemes and Partial Differential Equations, Second Edition is one of the few texts in the field to not only present the theory of stability in a rigorous and clear manner but also to discuss the theory of initial-boundary value problems in relation to finite difference schemes.

Fourier analysis is used throughout the book to. Nonstandard Finite Difference Scheme 3 Finite Difference Approaches To transform a continuous-time model into a discrete one, the continuous variable t2[0;1) must be replaced by the discrete variable n2N and the variable ˘must take discrete values ˘ n.

The result is a difference equation. Let f: Rn. Rnconsider a sequence f˘ ng 1 n=0. Nonstandard finite difference schemes for conservation laws preserving the property of diminishing total variation of the solution are proposed.

Computationally simple implicit schemes are derived by using nonlocal approximation of nonlinear by: 6. Non-standard finite-difference modelling FIG. 2. The central finite-difference slope is shown in red, but is shifted to go through the point at which it applies.

For comparison, the forward finite-difference in magenta is also shown. The central finite-difference is obviously much closer to the true analytic derivative plotted in blue.Since in general, these requirements are not satisfied in the application of most standard finite difference schemes, the concept of non-standard finite difference schemes was proposed for the first time by Mickens in as a solution to the numerical instability.

It File Size: KB.One way to avoiding this disadvantage is to employ nonstandard finite difference (NSFD) schemes [1,2,7,10,15,19,23]. More precisely, NSFDs in addition to the usual properties of consistency, stability and hence convergency, produce numerical solutions which Author: M.

Mehdizadeh Khalsaraei, Sh. Heydari, L. Davari Algoo.