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Ronald E Mickens
Advances In The Applications Of Nonstandard Finite Difference Schemes
非标准有限差分格式的应用进展
World Scientific Publishing Company Ronald E Mickens
ISBN：9789812564047，出版年：2005，中图分类号：O15

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.

Standard Commands for Programmable Instruments Variance decomposition of forecast errors Generic programming Projective invariance Common-method variance Finite difference method Joint application design Aspect-oriented programming Standard terminal arrival route Application-specific integrated circuit
Nonstandard Finite Difference Schemes: Methodology And Applications
非标准有限差分格式：方法与应用
World Scientific Publishing Company Ronald E Mickens
ISBN：9789811222535，出版年：2020，中图分类号：O15

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.

Finite difference method Common-method variance Variational method Applied element method Difference-map algorithm Gradient method Standard algorithms Multidisciplinary approach System design methodology Conception Method
Edward Bouchet: The First African-american Doctorate
爱德华·布切特：第一个非洲裔美国博士
World Scientific Publishing Company Ronald E Mickens
ISBN：9789810249090，出版年：2002，中图分类号：K81

Edward A Bouchet was the first African-American to receive the doctorate in any field of knowledge in the United States and that area was physics. He was granted the degree in 1876 from Yale University making him at that time one of the few persons to hold the physics doctorate from an American university. Bouchet played a significant role in the education of African-Americans during the last quarter of the 19th century through his teaching and mentoring activities at the Institute for Colored Youth in Philadelphia, Pennsylvania. He was one among a small number of African-Americans who achieved advanced training and education within decades of the American civil war. These people provided direction, leadership, and role models for what eventually became the civil/human rights movements. The year 2001 marks the 125th celebration of his receiving the doctorate degree. This book gives a summary of his life and career.

Primary physician Arzt patienten beziehung Arzt patient verhaltnis Physician self-referral Consultant physician Doctor–patient relationship History of Africa Portuguese East Africa Consulting Physician Admitting physician
Truly Nonlinear Oscillations: Harmonic Balance, Parameter Expansions, Iteration, And Averaging Methods
非线性振荡：谐波平衡，参数展开，迭代和平均法
World Scientific Publishing Company Ronald E Mickens
ISBN：9789814291651，出版年：2010，中图分类号：O15

This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of “truly nonlinear” (TNL) oscillator equations. The volume gives a general overview of the author's work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a direct comparison to be made among the various methods.The book is self-contained and therefore suitable for both classroom use and self-study by students and professionals who desire to learn, understand, and apply these technique to the field of nonlinear oscillations.

Asynchronous parallel algorithms Scalable parallel algorithms Asynchronous parallel computation Sequential parameter optimization Equilibrium unfolding Augmented Lagrangian method Adaptive resonance theory Parallel dynamics Non linear curve fitting Nonlinear dimensionality reduction
Applications Of Nonstandard Finite Difference Schemes
非标准差分格式的应用
World Scientific Publishing Company Ronald E Mickens
ISBN：9789810241339，出版年：2000，中图分类号：O15

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.

Joint application design Finite difference method Generic programming Common-method variance Standard Commands for Programmable Instruments Application software Application programmer Applicative programming language Semidefinite programming Projective invariance
Oscillations In Planar Dynamic Systems
平面动力系统的振动
World Scientific Publishing Company Ronald E Mickens
ISBN：9789810222925，出版年：1996，中图分类号：O3

This book provides a concise presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems. These systems model many important phenomena in the sciences and engineering. In addition to the usual perturbation procedures, the book gives the details of when and how to correctly apply the method of harmonic balance for both first-order and higher-order calculations. This procedure is rarely given or discussed fully in standard textbooks. The basic philosophy of the book stresses how to initiate and complete the calculation of approximate solutions. This is done by a clear presentation of necessary background materials and by the working out of many examples.

Dynamical friction Discrete dynamics Spin dynamics Slosh dynamics Universality (dynamical systems) Orbit Attitude and Maneuvering System Metafluid dynamics Aeration system Predetermined motion time system Fluid dynamics
Nonstandard Finite Difference Models Of Differential Equations
微分方程的非标准有限差分模型
World Scientific Publishing Company Ronald E Mickens
ISBN：9789810214586，出版年：1993，中图分类号：O15

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. A consequence of this result is that in general bigger step-sizes can often be used in actual calculations and/or finite difference schemes can be constructed that are conditionally stable in many instances whereas in using standard techniques no such schemes exist. The theoretical basis of this work is centered on the concepts of “exact” and “best” finite difference schemes. In addition, a set of rules is given for the discrete modeling of derivatives and nonlinear expressions that occur in differential equations. These rules often lead to a unique nonstandard finite difference model for a given differential equation.

Simultaneous equations model Primitive equation model Differential equation Integral equation model Equation-free modeling Stochastic differential equation Partial differential equation Mathematical model Trapezoidal rule (differential equations) Multi model inference
Mathematics And Science
数学与科学
World Scientific Publishing Company Ronald E Mickens
ISBN：9789810202330，出版年：1990，中图分类号：O15

The purpose of this review volume is to present the opinions of a number of distinguished individuals who have given careful thought as to why mathematics is so “unreasonably effective” when applied to the analysis of the natural sciences.

Mathematics Computational science Mathematics education Mathematical and theoretical biology Engineering mathematics Mathematical physics Mathematical chemistry Discrete mathematics Mathematical Computing Computational science education
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