Introduction to Numerical Methods in Differential Equations [Paperback]

This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.

This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. Includes more than 100 illustrations, exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.

The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, lets start with the expression di?erential equations. These are essential in science and engineering, because the laws of nature t- ically result in equations relating spatial and temporal changes in one or more variables.Todevelopanunderstandingofwhatisinvolvedin?ndingsolutions, the book begins with problems involving derivatives for only one independent variable, and these give rise to ordinary di?erential equations. Speci?cally, the ?rst chapter considers initial value problems (time derivatives), and the second concentrates on boundary value problems (space derivatives). In the succeeding four chapters problems involving both time and space derivatives, partial di?erential equations, are investigated. This brings us to the next expression in the title: numerical methods. This is a book about how to transform di?erential equations into problems that can be solved using a computer. The fact lóä