Introduction to Numerical Methods in Differential Equations (Paperback)

Mark H. Holmes

ISBN 10: 144192163X / ISBN 13: 9781441921635

Editore: Springer-Verlag New York Inc., New York, NY, 2010

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Paperback. 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 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9781441921635

Dati bibliografici

• Titolo: Introduction to Numerical Methods in Differential Equations (Paperback)
• Editore: Springer-Verlag New York Inc., New York, NY
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 144192163X
• ISBN 13: 9781441921635
• Rilegatura: Paperback
• Edizione: prima edizione
• Condizione: new

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Riassunto

This book shows students 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. An essential component of this approach is the extensive collection of exercises, which develop both the analytical and computational aspects of the material. Numerical methods for differential equations are important in a variety of disciplines: most laws of physics involve differential equations, as do the modern theories of financial assets. Moreover many computer animation methods are now grounded in physics-based rules and are heavily invested in differential equations. 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.

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