This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This third volume collects authoritative chapters covering several numerical aspects of fractional calculus, including time and space fractional derivatives, finite differences and finite elements, and spectral, meshless, and particle methods.
Engineers need hands-on experience in solving complex engineering problems with computers. This text introduces numerical methods and shows how to develop, analyze, and use them. A thorough and practical book, it is is intended as a first course in numerical analysis, primarily for beginning graduate students in engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods.
They will learn what factors affect accuracy, stability, and convergence. A special feature is the numerous examples and exercises that are included to give students first-hand experience. 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. The theoretical basis of this work is centered on the concepts of?
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. One purpose of this report is to present a mathematical procedure which can be used to study and compare various numerical methods for integrating ordinary differential equations.
This procedure is relatively simple, mathematically rigorous, and of such a nature that matters of interest in digital computations, such as machine memory and running time, can be weighed against the accuracy and stability provided by the method under consideration. Briefly, the procedure is as follows: 1 Find a single differential equation that is sufficiently representative this is fully defined in the report of an arbitrary number of nonhomogeneous, linear, ordinary differential equations with constant coefficients.
Conceptually there is nothing new in this procedure, but the particular development presented in this report does not appear to have been carried out before. Another purpose is to use the procedure just described to analyze a variety of numerical methods, ranging from classical, predictor-corrector systems to Runge-Kutta techniques and including various combinations of the two.
Written for undergraduates who require a familiarity with the principles behind numerical analysis, this classical treatment encompasses finite differences, least squares theory, and harmonic analysis.
Over 70 examples and exercises. Covers numerical analysis for mathematics students without neglecting practical aspects. The calculus of finite differences is here treated thoroughly and clearly by one of the leading American experts in the field of numerical analysis and computation.
The theory is carefully developed and applied to illustrative examples, and each chapter is followed by a set of helpful exercises. The book is especially designed for the use of actuarial students, statisticians, applied mathematicians, and any scientists forced to seek numerical solutions.
It presupposes only a knowledge of algebra, analytic geometry, trigonometry, and elementary calculus. The object is definitely practical, for while numerical calculus is based on the concepts of pure mathematics, it is recognized that the worker must produce a numerical result.
Originally published in Advanced embedding details, examples, and help! Reviewer: BudHelm - favorite favorite favorite favorite favorite - April 19, Subject: Invaluable piece Greetings! Thanks for sharing useful information.
I am thankful for the info , Does anyone know if my company might be able to get access to a sample a form copy to fill in? Reviewer: a e b - favorite favorite favorite favorite - September 8, Subject: he did more than Boolean Algebra These days George Boole is associated with Boolean logic, which is used in the design of digital computers.
And indeed he is responsible for Boolean Algebra. But Boole also did pioneering work in invariant theory, and produced this book on finite difference calculus. Finite difference calculus tends to be ignored in the 21st century. Yet this is the theoretical basis for summation of series once one gets beyond arithmetic and geometric series.
Back in the s I did a lot of work requiring summation of some very strange series. Finite difference calculus provided the tools to do that. At that time I used other reference books on the subject I did not purchase this book until the early s. But this book is an excellent summary of the applied side of the subject. Since the first edition of this book was , obviously there are a lot of developments not included.
Indeed, even by the time of the second edition , some flaws were obvious. But this gives a solid foundation.
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