Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance
We study the spatial discretisation of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients. The equation free term and the initial data are also allowed to grow. Under a nondegeneracy assumpti...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/801059 |
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| author | Fernando F. Gonçalves Maria Rosário Grossinho |
| author_facet | Fernando F. Gonçalves Maria Rosário Grossinho |
| author_sort | Fernando F. Gonçalves |
| collection | DOAJ |
| description | We study the spatial discretisation of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients. The equation free term and the initial data are also allowed to grow. Under a nondegeneracy assumption, we consider the PDE solvability in the framework of the variational approach and approximate in space the PDE problem's generalised solution, with the use of finite-difference methods. The rate of convergence is estimated. |
| format | Article |
| id | doaj-art-88ada32628784b59b8655170c195cf66 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-88ada32628784b59b8655170c195cf662025-02-03T01:22:16ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/801059801059Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to FinanceFernando F. Gonçalves0Maria Rosário Grossinho1CEMAPRE & Departmento de Matemática, ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, PortugalCEMAPRE & Departmento de Matemática, ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 Lisboa, PortugalWe study the spatial discretisation of the Cauchy problem for a multidimensional linear parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients. The equation free term and the initial data are also allowed to grow. Under a nondegeneracy assumption, we consider the PDE solvability in the framework of the variational approach and approximate in space the PDE problem's generalised solution, with the use of finite-difference methods. The rate of convergence is estimated.http://dx.doi.org/10.1155/2014/801059 |
| spellingShingle | Fernando F. Gonçalves Maria Rosário Grossinho Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance Abstract and Applied Analysis |
| title | Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance |
| title_full | Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance |
| title_fullStr | Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance |
| title_full_unstemmed | Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance |
| title_short | Spatial Approximation of Nondivergent Type Parabolic PDEs with Unbounded Coefficients Related to Finance |
| title_sort | spatial approximation of nondivergent type parabolic pdes with unbounded coefficients related to finance |
| url | http://dx.doi.org/10.1155/2014/801059 |
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