Numerical Partial Differential Equations: Finite Difference Methods

1. Front Matter

   Pages i-xx

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2. Prelude

   • J. W. Thomas

   Pages 1-4

3. Introduction to Finite Differences

   • J. W. Thomas

   Pages 5-39

4. Some Theoretical Considerations

   • J. W. Thomas

   Pages 41-95

5. Stability

   • J. W. Thomas

   Pages 97-145

6. Parabolic Equations

   • J. W. Thomas

   Pages 147-203

7. Hyperbolic Equations

   • J. W. Thomas

   Pages 205-259

8. Systems of Partial Differential Equations

   • J. W. Thomas

   Pages 261-360

9. Dispersion and Dissipation

   • J. W. Thomas

   Pages 361-426

10. Back Matter

    Pages 427-437

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This text will be divided into two books which cover the topic of numerical partial differential equations. Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student, this text offers a means of coming out of a course with a large number of methods which provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation.

• YellowSale2006
• adopted-textbook
• differential equation
• hyperbolic equation
• partial differential equation
• stability

"This important volume is the first part of a two-part textbook (the second part is entitled Conservation laws and elliptic equations). The text includes interesting homework problems that implement different aspects of most of the schemes discussed. The implementation aspect of this text includes a large amount of computing. Other useful aspects of computing included in this volume are symbolic computing and the use of graphics for analysis. Prerequisites suggested for using this book might include one semester of partial differential equations and some programming capability. This book will be a good reference text for students." -- MATHEMATICAL REVIEWS

• Department of Mathematics, Colorado State University, Fort Collins, USA

  J. W. Thomas

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