Highly Accurate Compact Finite Difference Method and its Applications - Couverture souple

Zhao, Jichao

 
9783639152470: Highly Accurate Compact Finite Difference Method and its Applications
Couverture souple
ISBN 10 : 3639152476 ISBN 13 : 9783639152470
Editeur : VDM Verlag, 2009

Synopsis

This book talks about the symbolic generation of finite difference schemes, especially so-called compact finite difference schemes, and their numerical applications to elliptic equations, integro-differential equations, the American option pricing problem, and cardiac tissue models. We take as a base Corless and Rokicki?s 1995 work on automatic generation of finite difference formulae and numerical integration formulae of univariate and bivariate problems. We then extend this methodology to any dimension. The new Maple routine FINDIF allows for automatic, symbolic discretization of various finite difference formulae, integration formulae, and computes formulae for truncation errors. Compact finite difference schemes are given for boundary value problems and elliptic partial differential equations. Compact finite difference methods are also used to solve efficiently integro-differential equations (IDE?s). Furthermore, we apply the method to solve the famous American option pricing problem and simulate the action potential propagation through two dimensional cardiac tissues. All simulation results demonstrate the compact finite difference method is a promising approach.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

This book talks about the symbolic generation of finite difference schemes, especially so-called compact finite difference schemes, and their numerical applications to elliptic equations, integro-differential equations, the American option pricing problem, and cardiac tissue models. We take as a base Corless and Rokicki?s 1995 work on automatic generation of finite difference formulae and numerical integration formulae of univariate and bivariate problems. We then extend this methodology to any dimension. The new Maple routine FINDIF allows for automatic, symbolic discretization of various finite difference formulae, integration formulae, and computes formulae for truncation errors. Compact finite difference schemes are given for boundary value problems and elliptic partial differential equations. Compact finite difference methods are also used to solve efficiently integro-differential equations (IDE?s). Furthermore, we apply the method to solve the famous American option pricing problem and simulate the action potential propagation through two dimensional cardiac tissues. All simulation results demonstrate the compact finite difference method is a promising approach.

Biographie de l'auteur

I obtained my Ph.D. degree in 2006 from the Department of Applied Mathematics at University of Western Ontario, Canada. Then I worked one year in INRIA, France as a postdoc fellow. Now I work on atrial computer modeling in Auckland University. My research focuses on numerical computation, and its application in Financial Mathematics and Biology.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag
Date d'édition
2009
Langue
anglais
ISBN 10 
3639152476
ISBN 13 
9783639152470
Reliure
Broché
Nombre de pages
172
Coordonnées du fabricant
non disponible
Personne responsable
non disponible