Introduction to Numerical Methods in Differential Equations

Holmes, Mark H. (Rensselaer Polytechnic Institute, Troy, NY, USA)

ISBN 10: 0387308911 / ISBN 13: 9780387308913

Published by Springer-Verlag New York Inc., 2006

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. Series: Texts in Applied Mathematics. Num Pages: 250 pages, 14 black & white tables, biography. BIC Classification: PBKJ. Category: (UU) Undergraduate. Dimension: 166 x 241 x 23. Weight in Grams: 536. . 2006. Hardback. . . . . Books ship from the US and Ireland. Seller Inventory # V9780387308913

Synopsis:

The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, let’s 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 differential equations into problems that can be solved using a computer.The fact is that computers are only able to solve discrete problems and generally do this using ?nite-precision arithmetic. What this means is that in deriving and then using a numerical algorithmthecorrectnessofthediscreteapproximationmustbeconsidered,as must the consequences of round-o? error in using ?oating-point arithmetic to calculatetheanswer.Oneoftheinterestingaspectsofthesubjectisthatwhat appears to be an obviously correct numerical method can result in complete failure. Consequently, although the book concentrates on the derivation and use of numerical methods, the theoretical underpinnings are also presented andusedinthedevelopment.

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Bibliographic Details

Title: Introduction to Numerical Methods in ...
Publisher: Springer-Verlag New York Inc.
Publication Date: 2006
Binding: Hardcover
Condition: New