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# π Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematics) by Randall Leveque β free pdf

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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:
**23 516 966** - 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...

This considerably extended and completely revised second edition incorporates many new developments in the thriving field of numerical methods for singularly perturbed differential equations. It provides a thorough foundation for the numerical analysis an...

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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Tag-based approaches were originally designed to increase the throughput of capillary sequencing, where concatemers of short sequences were first used in expression profiling. New Next Generation Sequencing methods largely extended the use of tag-based ap...

Talk in Action examines the language, identity, and interaction of social institutions, introducing students to the research methodology of Conversation Analysis. Features a unique focus on real-world applications of CA by examining four institutional dom...

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This book gathers together a selection of papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control held at the Paris Sorbonne, France, 10-12 July 2006. The main objective of the Workshop was to promote the exchange of ideas and exp...

Covering philosophical issues ranging from tattooed religious symbols to a feminist aesthetics of tattoo, Tattoos and Philosophy offers an enthusiastic analysis of inking that will lead readers to consider the nature of the tattooing arts in a new and pro...

Content: Chapter 1 Engaging Minds: Introducing Best Practices in Teaching Critical Thinking in Psychology (pages 1β8): Dana S. Dunn, Jane S. Halonen and Randolph A. SmithChapter 2 Critical Thinking: Needed Now More Than Ever (pages 9β21): Carole WadeChapt...

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Today more than ever before in the history of the poultry industry there is a concerted effort to improve the working relationship between the grower and the integrator. Teamwork in Poultry Production picks up wher Larry Cole's previous book, Communicatio...

Automatic speech recognition (ASR) systems are finding increasing use in everyday life. Many of the commonplace environments where the systems are used are noisy, for example users calling up a voice search system from a busy cafeteria or a street. This c...