Share

Computer-Aided Analysis of Difference Schemes for Partial Differential Equations

2011-03-01 Science
Download Computer-Aided Analysis of Difference Schemes for Partial Differential Equations PDF Online Free

Author :
Release : 2011-03-01
Genre : Science
Kind : eBook
Book Rating : 850/5 ( reviews)

GET EBOOK


Book Synopsis Computer-Aided Analysis of Difference Schemes for Partial Differential Equations by : Victor G. Ganzha

Download or read book Computer-Aided Analysis of Difference Schemes for Partial Differential Equations written by Victor G. Ganzha. This book was released on 2011-03-01. Available in PDF, EPUB and Kindle. Book excerpt: Advances in computer technology have conveniently coincided withtrends in numerical analysis toward increased complexity ofcomputational algorithms based on finite difference methods. It isno longer feasible to perform stability investigation of thesemethods manually--and no longer necessary. As this book shows,modern computer algebra tools can be combined with methods fromnumerical analysis to generate programs that will do the jobautomatically. Comprehensive, timely, and accessible--this is the definitivereference on the application of computerized symbolic manipulationsfor analyzing the stability of a wide range of difference schemes.In particular, it deals with those schemes that are used to solvecomplex physical problems in areas such as gas dynamics, heat andmass transfer, catastrophe theory, elasticity, shallow watertheory, and more. Introducing many new applications, methods, and concepts,Computer-Aided Analysis of Difference Schemes for PartialDifferential Equations * Shows how computational algebra expedites the task of stabilityanalysis--whatever the approach to stability investigation * Covers ten different approaches for each stability method * Deals with the specific characteristics of each method and itsapplication to problems commonly encountered by numerical modelers * Describes all basic mathematical formulas that are necessary toimplement each algorithm * Provides each formula in several global algebraic symboliclanguages, such as MAPLE, MATHEMATICA, and REDUCE * Includes numerous illustrations and thought-provoking examplesthroughout the text For mathematicians, physicists, and engineers, as well as forpostgraduate students, and for anyone involved with numericsolutions for real-world physical problems, this book provides avaluable resource, a helpful guide, and a head start ondevelopments for the twenty-first century.

Partial Differential Equations

2023-01-01 Mathematics
Download Partial Differential Equations PDF Online Free

Author :
Release : 2023-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 79X/5 ( reviews)

GET EBOOK


Book Synopsis Partial Differential Equations by : Wolfgang Arendt

Download or read book Partial Differential Equations written by Wolfgang Arendt. This book was released on 2023-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach. A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses on finite difference and finite element methods. Computer-aided calculation with MapleTM completes the book. Throughout, three fundamental examples are studied with different tools: Poisson’s equation, the heat equation, and the wave equation on Euclidean domains. The Black–Scholes equation from mathematical finance is one of several opportunities for extension. Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.

Finite Difference Schemes and Partial Differential Equations

1989-09-28 Juvenile Nonfiction
Download Finite Difference Schemes and Partial Differential Equations PDF Online Free

Author :
Release : 1989-09-28
Genre : Juvenile Nonfiction
Kind : eBook
Book Rating : /5 ( reviews)

GET EBOOK


Book Synopsis Finite Difference Schemes and Partial Differential Equations by : John C. Strikwerda

Download or read book Finite Difference Schemes and Partial Differential Equations written by John C. Strikwerda. This book was released on 1989-09-28. Available in PDF, EPUB and Kindle. Book excerpt:

Analysis of Finite Difference Schemes

2013-10-22 Mathematics
Download Analysis of Finite Difference Schemes PDF Online Free

Author :
Release : 2013-10-22
Genre : Mathematics
Kind : eBook
Book Rating : 606/5 ( reviews)

GET EBOOK


Book Synopsis Analysis of Finite Difference Schemes by : Boško S. Jovanović

Download or read book Analysis of Finite Difference Schemes written by Boško S. Jovanović. This book was released on 2013-10-22. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.

Finite Difference Methods for Ordinary and Partial Differential Equations

2007-01-01 Mathematics
Download Finite Difference Methods for Ordinary and Partial Differential Equations PDF Online Free

Author :
Release : 2007-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 839/5 ( reviews)

GET EBOOK


Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque

Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque. This book was released on 2007-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

You may also like...