Finite Difference Methods for Ordinary and Partial Differential Equations

Viser: Finite Difference Methods for Ordinary and Partial Differential Equations - Steady-State and Time-Dependent Problems

Steady-State and Time-Dependent Problems

Randall J. LeVeque

(2007)

Sprog: Engelsk

Society for Industrial and Applied Mathematics

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Paperback: 354 sider
Udgiver: Society for Industrial and Applied Mathematics (Juli 2007)
ISBN: 9780898716290

Beskrivelse
Indhold

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. Exercises and student projects are available on the book's webpage, along with Matlab mfiles for implementing methods. Readers will gain an understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another, and their practical implications. The author provides a foundation from which students can approach more advanced topics.

Preface
Part I: Boundary Value Problems and Iterative Methods.
Chapter 1: Finite Difference Approximations
Chapter 2: Steady States and Boundary Value Problems
Chapter 3: Elliptic Equations
Chapter 4: Iterative Methods for Sparse Linear Systems
Part II: Initial Value Problems.
Chapter 5: The Initial Value Problem for Ordinary Differential Equations
Chapter 6: Zero-Stability and Convergence for Initial Value Problems
Chapter 7: Absolute Stability for Ordinary Differential Equations
Chapter 8: Stiff Ordinary Differential Equations
Chapter 9: Diffusion Equations and Parabolic Problems
Chapter 10: Advection Equations and Hyperbolic Systems
Chapter 11: Mixed Equations Appendix A: Measuring Errors Appendix B: Polynomial Interpolation and Orthogonal Polynomials Appendix C: Eigenvalues and Inner-Product Norms Appendix D: Matrix Powers and Exponentials Appendix E: Partial Differential Equations Bibliography Index.