Finite Difference Methods for Ordinary and Partial Differential Equations by Randall LeVeque
Finite Difference Methods for ODEs and PDEs - Table of Contents
- PART-I BOUNDARY VALUE PROBLEMS AND ITERATIVE METHODS
- 1. Finite Difference Approximations
- 2. Steady States and Boundary Value Problems
- 3. Elliptic Equations
- 4. Iterative Methods for Sparse Linear Systems
- PART-II INITIAL VALUE PROBLEMS
- 5. The Initial Value Problem for ODEs
- 6. Zero-Stability and Convergence for Initial Value Problems
- 7. Absolute Stability for ODEs
- 8. Stiff ODEs
- 9. Diffusion Equations and Parabolic Problems
- 10. Advection Equations and Hyperbolic Systems
- 11. Mixed Equations
- PART-III APPENDICES
- 12. Measuring Errors
- 13. Polynomial Interpolation and Orthogonal Polynomials
- 14. Eigenvalues and Inner Product Norms
- 15. Matrix Powers and Exponentials
- 16. Partial Differential Equations
What You Will Learn in Finite Difference Methods for ODEs and PDEs
This textbook focuses deeply on how finite difference methods for ordinary and partial differential equations are constructed, rigorously analyzed, and practically applied to real-world engineering problems. Written in an accessible, student-friendly style, the author perfectly balances essential mathematical theory with deep computational insight, making it an invaluable resource for applied mathematics and scientific computing.
The text carefully explains foundational ideas such as numerical stability, consistency, and convergence. It demonstrates how these core concepts determine whether a finite difference method book or scheme will deliver stable and reliable computational results. Randall LeVeque emphasizes understanding why methods work, rather than just forcing readers to memorize complex formulas.
Furthermore, the book highlights the close, interlocking connection between numerical methods for ODEs and PDEs, helping readers and researchers build a unified perspective of advanced numerical analysis. It serves as an excellent foundation for anyone studying finite difference schemes, partial differential equations, stability analysis, and computational experiments.
Book Details & Specifications
Title:
Finite Difference Methods for Ordinary and Partial Differential Equations by Randall LeVeque
Publisher:
University of Washington
Year:
1998
Pages:
230
Type:
PDF
Language:
English
ISBN-10 #:
0898716292
ISBN-13 #:
978-0898716290
License:
University Educational Resource
Amazon:
Amazon
About the Author: Randall J. LeVeque
The author Randall J. LeVeque
is a Professor in the Departments of Mathematics and Applied Mathematics at the University of Washington, Seattle. He is widely recognized for his major contributions to numerical analysis, finite difference methods, and advanced scientific computing. Currently serving as Professor Emeritus, his research focuses on developing reliable computational techniques for solving differential equations used across science and engineering.
Professor LeVeque is also globally known as the lead developer of Clawpack, an open-source software package designed for solving hyperbolic partial differential equations. Through his high-level research, dedicated teaching, and classic textbooks, he continues to play a key role in advancing computational mathematics and partial differential equations worldwide.
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