Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB
Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB® teaches readers how to numerically solve both ordinary and partial differential equations with ease. This innovative publication brings together a skillful treatment of MATLAB and programming alongside theory and modeling. By presenting these topics in tandem, the author enables and encourages readers to perform their own computer experiments, leading them to a more profound understanding of differential equations.
The text consists of three parts:
- Introduction to MATLAB and numerical preliminaries, which introduces readers to the software and itsgraphical capabilities and shows how to use it to write programs
- Ordinary Differential Equations
- Partial Differential Equations
All the tools needed to master using MATLAB to solve differential equations are provided and include:
- "Exercises for the Reader" that range from routine computations to more advanced conceptual and theoretical questions (solutions appendix included)
- Illustrative examples, provided throughout the text, that demonstrate MATLAB's powerful ability to solve differential equations
- Explanations that are rigorous, yet written in a very accessible, user-friendly style
- Access to an FTP site that includes downloadable files of all the programs developed in the text
This textbook can be tailored for courses in numerical differential equations and numerical analysis as well as traditional courses in ordinary and/or partial differential equations. All the material has been classroom-tested over the course of many years, with the result that any self-learner with an understanding of basic single-variable calculus can master this topic. Systematic use is made of MATLAB's superb graphical capabilities to display and analyze results. An extensive chapter on the finite element method covers enough practical aspects (including mesh generation) to enable the reader to numerically solve general elliptic boundary value problems. With its thorough coverage of analytic concepts, geometric concepts, programs and algorithms, and applications, this is an unsurpassed pedagogical tool.
PART I: INTRODUCTION TO MATLAB AND NUMERICAL PRELIMINARIES.
Chapter 1. MATLAB Basics.
Chapter 2. Basic Concepts of Numerical Analysis with Taylor’s Theorem.
Chapter 3. Introduction to M-Files.
Chapter 4. Programming in MATLAB.
Chapter 5. Floating Point Arithmetic and Error Analysis.
Chapter 6. Rootfinding.
Chapter 7. Matrices and Linear Systems.
PART II: ORDINARY DIFFERENTIAL EQUATIONS.
Chapter 8. Introduction to Differential Equations.
Chapter 9. Systems of First-Order Differential Equations and Higher-Order Differential Equations
Chapter 10. Boundary Value Problems for Ordinary Differential Equations.
PART III: PARTIAL DIFFERENTIAL EQUATIONS.
Chapter 11. Introduction to Partial Differential Equations.
Chapter 12. Hyperbolic and Parabolic Partial Differential Equations
Chapter 13. The Finite Element Method.
Appendix A: Introduction to MATLAB’s Symbolic Toolbox.
Appendix B: Solutions to All Exercises for the Reader.
MATLAB Command Index.