Finite Difference Methods for Ordinary and Partial Differential Equations

Steady-State and Time-Dependent Problems

Häftad, Engelska, 2007

Av Randall J. LeVeque, Randall J. Leveque, Randall J Leveque

949 kr

Slutsåld

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.

Produktinformation

Utgivningsdatum2007-07-30
Mått177 x 251 x 17 mm
Vikt625 g
FormatHäftad
SpråkEngelska
Antal sidor354
FörlagSociety for Industrial & Applied Mathematics,U.S.
ISBN9780898716290

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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.