Difference Equations from Differential Equations: 41 (Lecture Notes in Engineering, 41) - Tapa blanda

James Lick, Wilbert

 
9783540507390: Difference Equations from Differential Equations: 41 (Lecture Notes in Engineering, 41)
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ISBN 10: 3540507396 ISBN 13: 9783540507390
Editorial: Springer Berlin Heidelberg, 1989

Sinopsis

In computational mechanics, the first and quite often the most difficult part of a problem is the correct formulation of the problem. This is usually done in terms of differential equations. Once this formulation is accomplished, the translation of the governing differential equations into accurate, stable, and physically realistic difference equations can be a formidable task. By comparison, the numerical evaluation of these difference equations in order to obtain a solution is usually much simpler. The present notes are primarily concerned with the second task, that of deriving accurate, stable, and physically realistic difference equations from the governing differential equations. Procedures for the numerical evaluation of these difference equations are also presented. In later applications, the physical formulation of the problem and the properties of the numerical solution, especially as they are related to the numerical approximations inherent in the solution, are discussed. There are numerous ways to form difference equations from differential equations.

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Reseña del editor

In computational mechanics, the first and quite often the most difficult part of a problem is the correct formulation of the problem. This is usually done in terms of differential equations. Once this formulation is accomplished, the translation of the governing differential equations into accurate, stable, and physically realistic difference equations can be a formidable task. By comparison, the numerical evaluation of these difference equations in order to obtain a solution is usually much simpler. The present notes are primarily concerned with the second task, that of deriving accurate, stable, and physically realistic difference equations from the governing differential equations. Procedures for the numerical evaluation of these difference equations are also presented. In later applications, the physical formulation of the problem and the properties of the numerical solution, especially as they are related to the numerical approximations inherent in the solution, are discussed. There are numerous ways to form difference equations from differential equations.

Reseña del editor

The primary purpose of this text is to illustrate the derivation of difference equations from differential equations using the volume integral method. In this method, the region of interest is divided into finite volume elements. The governing equations are then integrated over each of these elements. In order to form a difference equation, the terms in the resulting equations must be analytically approximated as well as possible. Various approaches to do this, including Taylor series expansions, have been developed and are illustrated in the text. The notes illustrate the applications of these ideas to ordinary and partial differential equations as well as some more specific applied problems. They have been used for an introductory course on numerical methods at the graduate level at the University of California, Santa Barbara.

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Editorial
Springer Berlin Heidelberg
Año de publicación
1989
Idioma
Inglés
ISBN 10 
3540507396
ISBN 13 
9783540507390
Encuadernación
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Número de páginas
300
Contacto del fabricante
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Alemania

Otras ediciones populares con el mismo título

9783642837029: Difference Equations from Differential Equations

Edición Destacada

ISBN 10:  3642837026 ISBN 13:  9783642837029
Editorial: Springer, 2011
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