Computer Aided Analysis Of Difference Schemes For Partial Differential Equations

Author : Victor G. Ganzha,E. V. Vorozhtsov
Publisher : John Wiley & Sons
Page : 458 pages
File Size : 49,8 Mb
Release : 2011-03-01
Category : Science
ISBN : 9781118030851

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Computer-Aided Analysis of Difference Schemes for Partial Differential Equations by Victor G. Ganzha,E. V. Vorozhtsov Pdf

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.

Author : Wolfgang Arendt,Karsten Urban
Publisher : Springer Nature
Page : 463 pages
File Size : 41,8 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 9783031133794

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Partial Differential Equations by Wolfgang Arendt,Karsten Urban Pdf

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.

Author : Boško S. Jovanović,Endre Süli
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 46,9 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9781447154600

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Analysis of Finite Difference Schemes by Boško S. Jovanović,Endre Süli Pdf

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.

Author : Ronghua Li,Zhongying Chen,Wei Wu
Publisher : CRC Press
Page : 472 pages
File Size : 44,7 Mb
Release : 2000-01-03
Category : Mathematics
ISBN : 9781482270211

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Generalized Difference Methods for Differential Equations by Ronghua Li,Zhongying Chen,Wei Wu Pdf

This text presents a comprehensive mathematical theory for elliptic, parabolic, and hyperbolic differential equations. It compares finite element and finite difference methods and illustrates applications of generalized difference methods to elastic bodies, electromagnetic fields, underground water pollution, and coupled sound-heat flows.

Author : Peter W. Hawkes
Publisher : Academic Press
Page : 479 pages
File Size : 55,5 Mb
Release : 2001-07-05
Category : Technology & Engineering
ISBN : 9780080526218

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Advances in Imaging and Electron Physics by Peter W. Hawkes Pdf

Advances in Imaging and Electron Physics merges two long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. This series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.

Author : Matthew England,Wolfram Koepf,Timur M. Sadykov,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher : Springer
Page : 479 pages
File Size : 52,9 Mb
Release : 2019-08-15
Category : Computers
ISBN : 9783030268312

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Computer Algebra in Scientific Computing by Matthew England,Wolfram Koepf,Timur M. Sadykov,Werner M. Seiler,Evgenii V. Vorozhtsov Pdf

This book constitutes the refereed proceedings of the 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019, held in Moscow, Russia, in August 2019. The 28 full papers presented together with 2 invited talks were carefully reviewed and selected from 44 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CASs in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.

Author : Jan A. Spriet,G. C. Vansteenkiste
Publisher : Unknown
Page : 510 pages
File Size : 45,7 Mb
Release : 1982
Category : Computer simulation
ISBN : UCAL:B4392278

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Computer-aided Modelling and Simulation by Jan A. Spriet,G. C. Vansteenkiste Pdf

A comprehensive overview of the major options and facilities that concern the model simulation builder.

Author : Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher : Springer
Page : 379 pages
File Size : 40,5 Mb
Release : 2018-09-03
Category : Computers
ISBN : 9783319996394

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Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov Pdf

This book constitutes the proceedings of the 20th International Workshop on Computer Algebra in Scientific Computing, CASC 2018, held in Lille, France, in September 2018. The 24 full papers of this volume presented with an abstract of an invited talk and one paper corresponding to another invited talk were carefully reviewed and selected from 29 submissions. They deal with cutting-edge research in all major disciplines of computer algebra in sciences such as physics, chemistry, life sciences, and engineering. Chapter “Positive Solutions of Systems of Signed Parametric Polynomial Inequalities” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 55,9 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898717833

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Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque Pdf

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.

Author : Ulrich Langer,Peter Paule
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 51,6 Mb
Release : 2011-11-19
Category : Mathematics
ISBN : 9783709107942

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Numerical and Symbolic Scientific Computing by Ulrich Langer,Peter Paule Pdf

The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.

Author : Victor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642602184

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Computer Algebra in Scientific Computing CASC’99 by Victor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov Pdf

The development of powerful computer algebra systems has considerably ex tended the scope of problems of scientific computing which can now be solved successfully with the aid of computers. However, as the field of applications of computer algebra in scientific computing becomes broader and more complex, there is a danger of separation between theory, systems, and applications. For this reason, we felt the need to bring together the researchers who now ap ply the tools of computer algebra for the solution of problems in scientific computing, in order to foster new and closer interactions. CASC'99 is the second conference devoted to applications of computer al gebra in scientific computing. The first conference in this sequence, CASC'98, was held 20-24 April 1998 in St. Petersburg, Russia. This volume contains revised versions of the papers submitted by the par ticipants and accepted by the program committee after a thorough reviewing process. The collection of papers included in the proceedings covers various topics of computer algebra methods, algorithms and software applied to scien tific computing: symbolic-numeric analysis and solving differential equations, efficient computations with polynomials, groups, matrices and other related objects, special purpose programming environments, application to physics, mechanics, optics and to other areas. In particular, a significant group of papers deals with applications of com puter algebra methods for the solution of current problems in group theory, which mostly arise in mathematical physics.

Author : François Boulier,Matthew England,Timur M. Sadykov,Evgenii V. Vorozhtsov
Publisher : Springer Nature
Page : 644 pages
File Size : 46,6 Mb
Release : 2020-10-17
Category : Computers
ISBN : 9783030600266

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Computer Algebra in Scientific Computing by François Boulier,Matthew England,Timur M. Sadykov,Evgenii V. Vorozhtsov Pdf

This book constitutes the refereed proceedings of the 22nd International Workshop on Computer Algebra in Scientific Computing, CASC 2020, held in Linz, Austria, in September 2020. The conference was held virtually due to the COVID-19 pandemic. The 34 full papers presented together with 2 invited talks were carefully reviewed and selected from 41 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CAS in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.

Author : Laurent Vulliet,Lyesse Laloui,Bernard Schrefler
Publisher : EPFL Press
Page : 446 pages
File Size : 54,5 Mb
Release : 2002-01-01
Category : Ingeniería ambiental
ISBN : 2880745152

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Environmental Geomechanics by Laurent Vulliet,Lyesse Laloui,Bernard Schrefler Pdf

Author : Gordon D. Smith
Publisher : Oxford University Press
Page : 356 pages
File Size : 47,5 Mb
Release : 1985
Category : Computers
ISBN : 0198596502

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Numerical Solution of Partial Differential Equations by Gordon D. Smith Pdf

Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.

Author : John C. Strikwerda
Publisher : SIAM
Page : 439 pages
File Size : 52,8 Mb
Release : 2007-09-20
Category : Mathematics
ISBN : 9780898716399

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Finite Difference Schemes and Partial Differential Equations by John C. Strikwerda Pdf

A unified and accessible introduction to the basic theory of finite difference schemes.