Download PDF Solving ODEs with MATLAB by L. F. SHAMPINE

Sinopsis

Ordinary differential equations (ODEs) are used throughout engineering, mathematics, and science to describe how physical quantities change, so an introductory course on elementary ODEs and their solutions is a standard part of the curriculum in these fields. Such a course provides insight, but the solution techniques discussed are generally unable to deal with the large, complicated, and nonlinear systems of equations seen in practice. This book is about solving ODEs numerically. Each of the authors has decades of experience in both industry and academia helping people like yourself solve problems. We begin in this chapter with a discussion of what is meant by a numerical solution with standard methods and, in particular, of what you can reasonably expect of standard software. In the chapters that follow, we discuss briefly the most popular methods for important classes of ODE problems. Examples are used throughout to show how to solve realistic problems. Matlab (2000) is used to solve nearly all these problems because it is a very convenient and widely used problem-solving environment (PSE) with quality solvers that are exceptionally easy to use. It is also such a high-level programming language that programs are short, making it practical to list complete programs for all the examples. We also include some discussion of software available in other computing environments. Indeed, each of the authors has written ODE solvers widely used in general scientific computing.

Content

1. Getting Started
2. Existence, Uniqueness, and Well-Posedness
3. Standard Form
4. Control of the Error
5. Qualitative Properties
6. Initial Value Problems
7. Numerical Methods for IVPs
8. Solving IVPs in Matlab
9. Boundary Value Problems
10. Boundary Conditions
11. Boundary Conditions at Singular Points
12. Boundary Conditions at Infinity
13. Numerical Methods for BVPs
14. Solving BVPs in Matlab
15. Delay Differential Equations
16. Numerical Methods for DDEs
17. Solving DDEs in Matlab
18. Other Kinds of DDEs and Software

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