Introduction to Numerical Methods in Differential Equations

Mark H. Holmes (Autor)

Buch | Softcover

239 Seiten

2010 | Softcover reprint of hardcover 1st ed. 2007
Springer-Verlag New York Inc.
978-1-4419-2163-5 (ISBN)

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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.

Initial Value Problems.- Two-Point Boundary Value Problems.- Diffusion Problems.- Advection Equation.- Numerical Wave Propagation.- Elliptic Problems.

Erscheint lt. Verlag	29.11.2010
Reihe/Serie	Texts in Applied Mathematics ; 52
Zusatzinfo	XI, 239 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4419-2163-X / 144192163X
ISBN-13	978-1-4419-2163-5 / 9781441921635
Zustand	Neuware