A clear and accessible introduction to the theory and numerical solution of partial differential equations, this text seamlessly blends mathematical rigor with computational practicality. Larsson and Thom�e present the fundamentals of elliptic, parabolic, and hyperbolic PDEs alongside finite difference and finite element methods, emphasizing convergence, stability, and error analysis. Designed for advanced undergraduates and graduate students in applied mathematics, engineering, or scientific computing, the book is ideal for those seeking to both understand the theory and implement reliable numerical algorithms for solving PDEs. ; 16.5x24.5x2.5cm ; ix,259,(1) pages.

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Bibliographic Details

Title: Partial Differential Equations with Numerical Methods - Texts in Applied Mathematics, 45
Publisher: Springer, New York, Berlin, Tokyo
Publication Date: 2003
Language: English
ISBN 10: 3540017720
ISBN 13: 9783540017721
Binding: Hardcover
Edition: (?); (?).
Condition: Near Fine
Dust Jacket Condition: No Dust Jacket

About this title

Synopsis

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. 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. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. 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. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

From the Back Cover

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.

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