Variable Step Size Adams Methods for BSDEs
For backward stochastic differential equations (BSDEs), we construct variable step size Adams methods by means of Itô–Taylor expansion, and these schemes are nonlinear multistep schemes. It is deduced that the conditions of local truncation errors with respect to Y and Z reach high order. The coeffi...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9799627 |
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| _version_ | 1832558010235355136 |
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| author | Qiang Han |
| author_facet | Qiang Han |
| author_sort | Qiang Han |
| collection | DOAJ |
| description | For backward stochastic differential equations (BSDEs), we construct variable step size Adams methods by means of Itô–Taylor expansion, and these schemes are nonlinear multistep schemes. It is deduced that the conditions of local truncation errors with respect to Y and Z reach high order. The coefficients in the numerical methods are inferred and bounded under appropriate conditions. A necessary and sufficient condition is given to judge the stability of our numerical schemes. Moreover, the high-order convergence of the schemes is rigorously proved. The numerical illustrations are provided. |
| format | Article |
| id | doaj-art-0659db1007eb44f5a156867b4c59efcf |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-0659db1007eb44f5a156867b4c59efcf2025-02-03T01:33:21ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/9799627Variable Step Size Adams Methods for BSDEsQiang Han0Zhongtai Securities Institute for Financial StudiesFor backward stochastic differential equations (BSDEs), we construct variable step size Adams methods by means of Itô–Taylor expansion, and these schemes are nonlinear multistep schemes. It is deduced that the conditions of local truncation errors with respect to Y and Z reach high order. The coefficients in the numerical methods are inferred and bounded under appropriate conditions. A necessary and sufficient condition is given to judge the stability of our numerical schemes. Moreover, the high-order convergence of the schemes is rigorously proved. The numerical illustrations are provided.http://dx.doi.org/10.1155/2021/9799627 |
| spellingShingle | Qiang Han Variable Step Size Adams Methods for BSDEs Journal of Mathematics |
| title | Variable Step Size Adams Methods for BSDEs |
| title_full | Variable Step Size Adams Methods for BSDEs |
| title_fullStr | Variable Step Size Adams Methods for BSDEs |
| title_full_unstemmed | Variable Step Size Adams Methods for BSDEs |
| title_short | Variable Step Size Adams Methods for BSDEs |
| title_sort | variable step size adams methods for bsdes |
| url | http://dx.doi.org/10.1155/2021/9799627 |
| work_keys_str_mv | AT qianghan variablestepsizeadamsmethodsforbsdes |