Finite Difference Methods for Differential Equations by Randall LeVeque

About this book :-
"Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems" by "Randall J. LeVeque" is a clear and practical introduction to numerical techniques used for solving differential equations on computers. The book focuses on how "finite difference methods" are constructed, analyzed, and applied to both ordinary and partial differential equations. It is written in a student-friendly style, balancing mathematical theory with real computational insight. The text carefully explains key ideas such as "stability", "consistency", and "convergence", showing how these concepts determine whether a numerical method will give reliable results. LeVeque emphasizes understanding "why" methods work, not just how to apply formulas. The book also highlights the close connection between numerical methods for ODEs and PDEs, helping readers build a unified perspective of numerical analysis. This book is widely used in applied mathematics, engineering, and scientific computing courses. It includes meaningful examples, exercises, and references to computational experiments that strengthen practical skills. Overall, it is an excellent foundation for anyone interested in "numerical analysis", "finite difference schemes", "partial differential equations", "stability analysis", and "scientific computing", making it valuable for both students and researchers.

Book Detail :-
Title: Finite Difference Methods for 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 Author :-
The author Randall J. LeVeque is a Professor in the Departments of Mathematics and Applied Mathematics at the University of Washington, Seattle. He was known for his major contributions to "numerical analysis", "finite difference methods", and "scientific computing". He served as Professor Emeritus of Applied Mathematics at the University of Washington, where he focused on developing reliable computational techniques for solving differential equations used in science and engineering. He is widely recognized as the lead developer of "Clawpack", an open-source software package for solving hyperbolic partial differential equations. Through his research, teaching, and textbooks, LeVeque has played a key role in advancing "computational mathematics" and "partial differential equations", influencing both academic research and real-world applications.

Book 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

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