A comparison of numerical methods to solve fractional partial differential equations

A comparison of numerical methods to solve fractional partial differential equations

A comparison of two numerical methods - ¯nite di®erence and Adomian decomposition method (ADM) - to solve a variety of fractional partial dif- ferential equations that occur in ¯nance are investigated. These fractional partial di®erential equations fall into the class of L¶evy models. They are k...

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Main Author: Marom, Ofir
Format: Others
Language:en
Published: 2010
Online Access:http://hdl.handle.net/10539/7682
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spelling ndltd-netd.ac.za-oai-union.ndltd.org-wits-oai-wiredspace.wits.ac.za-10539-76822019-05-11T03:42:06Z A comparison of numerical methods to solve fractional partial differential equations Marom, Ofir A comparison of two numerical methods - ¯nite di®erence and Adomian decomposition method (ADM) - to solve a variety of fractional partial dif- ferential equations that occur in ¯nance are investigated. These fractional partial di®erential equations fall into the class of L¶evy models. They are known as the Finite Moment Log Stable (FMLS), CGMY and the extended Koponen (KoBol) models. Convergence criteria for these models under the numerical methods are studied. ADM fails to accurately price a claim writ- ten on these models. However, the ¯nite di®erence scheme works well for the FMLS and KoBol models. 2010-03-15T11:44:26Z 2010-03-15T11:44:26Z 2010-03-15T11:44:26Z Thesis http://hdl.handle.net/10539/7682 en application/pdf
collection NDLTD
language en
format Others
sources NDLTD
description A comparison of two numerical methods - ¯nite di®erence and Adomian decomposition method (ADM) - to solve a variety of fractional partial dif- ferential equations that occur in ¯nance are investigated. These fractional partial di®erential equations fall into the class of L¶evy models. They are known as the Finite Moment Log Stable (FMLS), CGMY and the extended Koponen (KoBol) models. Convergence criteria for these models under the numerical methods are studied. ADM fails to accurately price a claim writ- ten on these models. However, the ¯nite di®erence scheme works well for the FMLS and KoBol models.
author Marom, Ofir
spellingShingle Marom, Ofir
A comparison of numerical methods to solve fractional partial differential equations
author_facet Marom, Ofir
author_sort Marom, Ofir
title A comparison of numerical methods to solve fractional partial differential equations
title_short A comparison of numerical methods to solve fractional partial differential equations
title_full A comparison of numerical methods to solve fractional partial differential equations
title_fullStr A comparison of numerical methods to solve fractional partial differential equations
title_full_unstemmed A comparison of numerical methods to solve fractional partial differential equations
title_sort comparison of numerical methods to solve fractional partial differential equations
publishDate 2010
url http://hdl.handle.net/10539/7682
work_keys_str_mv AT maromofir acomparisonofnumericalmethodstosolvefractionalpartialdifferentialequations
AT maromofir comparisonofnumericalmethodstosolvefractionalpartialdifferentialequations
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