# Partial Differential Equations with Numerical Methods

Part of the Texts in Applied Mathematics book series (TAM, volume 45)

Part of the Texts in Applied Mathematics book series (TAM, volume 45)

The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.

Boundary value problem Sobolev space elliptic equation finite difference method finite element method hyperbolic equation parabolic equation partial differential equation

- DOI https://doi.org/10.1007/978-3-540-88706-5
- Copyright Information Springer Berlin Heidelberg 2003
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-88705-8
- Online ISBN 978-3-540-88706-5
- Series Print ISSN 0939-2475
- About this book