Texts in Applied Mathematics - 44: Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Peter Knabner

ISBN 10: 1441930043 / ISBN 13: 9781441930040

Editore: Springer, 2010

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Leichte Abnutzungen; Gebogener Buchrücken. Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in - search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as nume- cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.

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Dati bibliografici

• Titolo: Texts in Applied Mathematics - 44: Numerical Methods for Elliptic and Parabolic Partial Differential Equations
• Editore: Springer
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 1441930043
• ISBN 13: 9781441930040
• Rilegatura: Softcover
• Condizione: Fine

Descrizione articolo

Riassunto

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Contenuti

For Example: Modelling Processes in Porous Media with Differential Equations * For the Beginning: The Finite Difference Method for the Poisson Equation * The Finite Element Method for the Poisson Equation * The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order * Grid Generation and A Posteriori Error Estimation * Iterative Methods for Systems of Linear Equations * The Finite Volume Method * Discretization Methods for Parabolic Initial Boundary Value Problems * Iterative Methods for Nonlinear Equations * Discretization Methods for Convection-Dominated Problems * Appendices