Advances In The Applications Of Nonstandard Finite Diffference Schemes
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Applications Of Nonstandard Finite Difference Schemes
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Author : Ronald E Mickens
language : en
Publisher: World Scientific
Release Date : 2000-03-29
Applications Of Nonstandard Finite Difference Schemes written by Ronald E Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-29 with Mathematics categories.
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 subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection-diffusion-reaction equations that arise in groundwater pollution and scattering of electromagnetic waves using Maxwell's equations. Chapter 4 examines certain mathematical issues related to the nonstandard discretization of competitive and cooperative models for ecology. Chapter 5 discusses exactness, stability properties, and the symplecticity of various schemes including the conditions for which Runge-Kutta methods are exact. The application chapters illustrate well the power of nonstandard methods. In particular, for the same accuracy as obtained by standard techniques, larger step sizes can be used.This volume will satisfy the needs of scientists, engineers, and mathematicians who wish to know how to construct nonstandard schemes and see how these are applied to obtain numerical solutions of the differential equations which arise in the study of nonlinear dynamical systems modeling important physical phenomena.
Advances In The Applications Of Nonstandard Finite Difference Schemes
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Author : Ronald E Mickens
language : en
Publisher: World Scientific
Release Date : 2005-10-25
Advances In The Applications Of Nonstandard Finite Difference Schemes written by Ronald E Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-25 with Mathematics categories.
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 sciences. These methods had their genesis in the work of Mickens in the 1990's and are now beginning to be widely studied and applied by other researchers. The importance of the book derives from its clear and direct explanation of NSFD in the introductory chapter along with a broad discussion of the future directions needed to advance the topic.
Advances In The Applications Of Nonstandard Finite Diffference Schemes
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Author : Ronald E. Mickens
language : en
Publisher: World Scientific
Release Date : 2005
Advances In The Applications Of Nonstandard Finite Diffference Schemes written by Ronald E. Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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 sciences. These methods had their genesis in the work of Mickens in the 1990''s and are now beginning to be widely studied and applied by other researchers. The importance of the book derives from its clear and direct explanation of NSFD in the introductory chapter along with a broad discussion of the future directions needed to advance the topic.
Advances In The Applications Of Nonstandard Finite Diffference Schemes
DOWNLOAD
Author : Ronald E. Mickens
language : en
Publisher: World Scientific
Release Date : 2005
Advances In The Applications Of Nonstandard Finite Diffference Schemes written by Ronald E. Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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 sciences. These methods had their genesis in the work of Mickens in the 1990's and are now beginning to be widely studied and applied by other researchers. The importance of the book derives from its clear and direct explanation of NSFD in the introductory chapter along with a broad discussion of the future directions needed to advance the topic.
Nonstandard Finite Difference Schemes Methodology And Applications
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Author : Ronald E Mickens
language : en
Publisher: World Scientific
Release Date : 2020-11-11
Nonstandard Finite Difference Schemes Methodology And Applications written by Ronald E Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-11 with Mathematics categories.
This second edition of Nonstandard Finite Difference Models of Differential Equations provides an update on the progress made in both the theory and application of the NSFD methodology during the past two and a half decades. In addition to discussing details related to the determination of the denominator functions and the nonlocal discrete representations of functions of dependent variables, we include many examples illustrating just how this should be done.Of real value to the reader is the inclusion of a chapter listing many exact difference schemes, and a chapter giving NSFD schemes from the research literature. The book emphasizes the critical roles played by the 'principle of dynamic consistency' and the use of sub-equations for the construction of valid NSFD discretizations of differential equations.
Advanced Numerical Methods For Differential Equations
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Author : Harendra Singh
language : en
Publisher: CRC Press
Release Date : 2021-06-25
Advanced Numerical Methods For Differential Equations written by Harendra Singh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-25 with Mathematics categories.
Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.
Mathematics Of Continuous And Discrete Dynamical Systems
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Author : Abba B. Gumel
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-18
Mathematics Of Continuous And Discrete Dynamical Systems written by Abba B. Gumel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-18 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations, in honor of Ronald Mickens's 70th birthday, held January 9-10, 2013, in San Diego, CA. Included are papers on design and analysis of discrete-time and continuous-time dynamical systems arising in the natural and engineering sciences, in particular, the design of robust nonstandard finite-difference methods for solving continuous-time ordinary and partial differential equation models, the analytical and numerical study of models that undergo nonlinear oscillations, as well as the design of deterministic and stochastic models for epidemiological and ecological processes. Some of the specific topics covered in the book include the analysis of deterministic and stochastic SIR-type models, the assessment of cost-effectiveness of vaccination problems, finite-difference methods for oscillatory dynamical systems (including the Schrödinger equation and Brusselator system), the design of exact and elementary stable finite-difference methods, the study of a two-patch model with Allee effects and disease-modified fitness, the study of the delay differential equation model with application to circadian rhythm and the application of some special functions in the solutions of some problems arising in the natural and engineering sciences. A notable feature of the book is the collection of some relevant open problems, intended to help guide the direction of future research in the area.
Numerical Methods And Applications
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Author : Ivan Georgiev
language : en
Publisher: Springer Nature
Release Date : 2023-05-15
Numerical Methods And Applications written by Ivan Georgiev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-15 with Mathematics categories.
This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Numerical Methods and Applications, NMA 2022, held in Borovets, Bulgaria, in August 2022.The 30 revised regular papers presented were carefully reviewed and selected from 38 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.
Exact Finite Difference Schemes
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Author : Sergey Lemeshevsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-09-26
Exact Finite Difference Schemes written by Sergey Lemeshevsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Mathematics categories.
Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography
Recent Progress In Computational Sciences And Engineering 2 Vols
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Author : Theodore Simos
language : en
Publisher: CRC Press
Release Date : 2019-05-07
Recent Progress In Computational Sciences And Engineering 2 Vols written by Theodore Simos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Computers categories.
This volume brings together selected contributed papers presented at the International Conference of Computational Methods in Science and Engineering (ICCMSE 2006), held in Chania, Greece, October 2006. The conference aims to bring together computational scientists from several disciplines in order to share methods and ideas. The ICCMSE is unique in its kind. It regroups original contributions from all fields of the traditional Sciences, Mathematics, Physics, Chemistry, Biology, Medicine and all branches of Engineering. It would be perhaps more appropriate to define the ICCMSE as a conference on computational science and its applications to science and engineering. Topics of general interest are: Computational Mathematics, Theoretical Physics and Theoretical Chemistry. Computational Engineering and Mechanics, Computational Biology and Medicine, Computational Geosciences and Meteorology, Computational Economics and Finance, Scientific Computation. High Performance Computing, Parallel and Distributed Computing, Visualization, Problem Solving Environments, Numerical Algorithms, Modelling and Simulation of Complex System, Web-based Simulation and Computing, Grid-based Simulation and Computing, Fuzzy Logic, Hybrid Computational Methods, Data Mining, Information Retrieval and Virtual Reality, Reliable Computing, Image Processing, Computational Science and Education etc. More than 800 extended abstracts have been submitted for consideration for presentation in ICCMSE 2005. From these 500 have been selected after international peer review by at least two independent reviewers.