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Finite difference methods with an implicit scheme
Taschenbuch von Pascal Sturm
Sprache: Englisch

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Beschreibung
Seminar paper from the year 2016 in the subject Mathematics - Miscellaneous, grade: 1,0, University of Tubingen, language: English, abstract: Using an explicit scheme for an application of finite difference methods may lead to stability issues. If one wants to increase the accuracy by raising the number of spatial grid points, the number of time intervals have to be increased to a certain extent in order to sustain a converging behavior.

As for quite accurate results ridiculously many grid points in time are needed, the practical use of the explicit scheme is rather limited due to high computational effort. Implicit methods for finite difference methods are designed to overcome these stability limitations imposed by the already mentioned convergence restrictions. Since such methods are unconditionally stable, both accuracy and limited computational effort can be combined.

This text offers an introductory treatment of Finite Difference Methods employing an implicit scheme. It includes a theoretical derivation of the implicit scheme and the Crank-Nicolson scheme, a numerical application to European puts as well as a theoretical discussion and comparison of the truncation error for both schemes. Finally, Richard-Extrapolation is introduced as a nice tool for lowering the truncation error.
Seminar paper from the year 2016 in the subject Mathematics - Miscellaneous, grade: 1,0, University of Tubingen, language: English, abstract: Using an explicit scheme for an application of finite difference methods may lead to stability issues. If one wants to increase the accuracy by raising the number of spatial grid points, the number of time intervals have to be increased to a certain extent in order to sustain a converging behavior.

As for quite accurate results ridiculously many grid points in time are needed, the practical use of the explicit scheme is rather limited due to high computational effort. Implicit methods for finite difference methods are designed to overcome these stability limitations imposed by the already mentioned convergence restrictions. Since such methods are unconditionally stable, both accuracy and limited computational effort can be combined.

This text offers an introductory treatment of Finite Difference Methods employing an implicit scheme. It includes a theoretical derivation of the implicit scheme and the Crank-Nicolson scheme, a numerical application to European puts as well as a theoretical discussion and comparison of the truncation error for both schemes. Finally, Richard-Extrapolation is introduced as a nice tool for lowering the truncation error.
Details
Erscheinungsjahr: 2017
Fachbereich: Allgemeines
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: 40 S.
ISBN-13: 9783668526075
ISBN-10: 3668526079
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Sturm, Pascal
Auflage: 1. Auflage
Hersteller: GRIN Verlag
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 210 x 148 x 4 mm
Von/Mit: Pascal Sturm
Erscheinungsdatum: 20.09.2017
Gewicht: 0,073 kg
Artikel-ID: 109751407
Details
Erscheinungsjahr: 2017
Fachbereich: Allgemeines
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: 40 S.
ISBN-13: 9783668526075
ISBN-10: 3668526079
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Sturm, Pascal
Auflage: 1. Auflage
Hersteller: GRIN Verlag
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 210 x 148 x 4 mm
Von/Mit: Pascal Sturm
Erscheinungsdatum: 20.09.2017
Gewicht: 0,073 kg
Artikel-ID: 109751407
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