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# ðŸ“™ Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematics) by Randall Leveque â€” free epub

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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.**About book:**

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The book is organized into two main sections and a set of appendices. Part I addresses steady-state boundary value problems, starting with two-point boundary value problems in one dimension, followed by coverage of elliptic problems in two and three dimensions. It concludes with a chapter on iterative methods for large sparse linear systems that emphasizes systems arising from difference approximations. Part II addresses time-dependent problems, starting with the initial value problem for ODEs, moving on to initial boundary value problems for parabolic and hyperbolic PDEs, and concluding with a chapter on mixed equations combining features of ODEs, parabolic equations, and hyperbolic equations. The appendices cover concepts pertinent to Parts I and II. Exercises and student projects, developed in conjunction with this book, are available on the book s webpage along with numerous MATLAB m-files.

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 and further explore the theory and/or use of finite difference methods according to their interests and needs.

**Audience: This book is designed as an introductory graduate-level textbook on finite difference methods and their analysis. It is also appropriate for researchers who desire an introduction to the use of these methods.**

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** Contents: 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. **

- Series:
**Classics in Applied Mathematics** - Author:
**Randall Leveque** - Year:
**2007** - Publisher:
**SIAM, Society for Industrial and Applied Mathematics** - Language:
**English** - ISBN:
**0898716292,9780898716290**

- File size:
**23 503 278** - Format:
**pdf**

Security code:

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 ...

This book brings together ten papers presented at the Conference on Harmonic Analysis and Partial Differential Equations, held in April 1988 at Florida Atlantic University. The papers illuminate the relationship between harmonic analysis and partial diffe...

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Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and prob...

Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and prob...

The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain n...

In the first part of this EMS volume Yu.V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the ...

A Compendium of Partial Differential Equation Models presents numerical methods and associated computer codes in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs), one of the mostly widely used forms of mat...

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The only introduction into the exciting chemistry of Lanthanides and Actinides. The book is based on a number of courses on "f elements" The author has a long experience in teaching this field of chemistry Lanthanides have become very common elements in r...

Published by the American Geophysical Union as part of the Geophysical Monograph Series. Continental flood basalts, volcanic passive margins, and oceanic plateaus represent the largest known volcanic episodes on our planet, yet they are not easily explain...

Nutrition is particularly important in the healthy development of fish during their early-life stages. Understanding the unique nutritional needs of larval fish can improve the efficiency and quality of fish reared in a culture setting. Larval Fish Nutrit...

Here, the editor has gathered a team of international experts to present the latest advances in the field of laser imaging and manipulation techniques. The result is broad coverage of the interactions with biological samples to perform novel optical manip...

A completely revised and expanded one-volume legal resource for tax-exempt healthcare organizations A complete and up-to-date legal resource for tax-exempt healthcare organizations and their advisors, this Fourth Edition, equips you with a comprehensiv...

Praise for the law of tax-exempt organizations "Mr. Hopkins-just wanted to let you know how much I am getting from The Law of Tax-Exempt Organizations. It is exceptionally clear, well organized, and well written. It has been a huge help to both my clie...

Addressing product liability concerns and laws both in the U.S. and internationally, this book helps manufacturers and engineers develop and implement proactive processes that can reduce liability concerns and potential lawsuits. It discusses preventive m...

Content: Chapter 1 Definitions and Methods of Measurement (pages 1â€“53): Chapter 2 The Operation of Leadâ€“Acid Batteries (pages 59â€“113): Chapter 3 Internal Composition and Types of Leadâ€“Acid Batteries (pages 115â€“134): Chapter 4 Lead Batteries: Main Characte...