Numerical solution for stochastic heat equation with Neumann boundary conditions
In this article, we propose a new technique based on 2-D shifted Legendre poly?nomials through the operational matrix integration method to find the numeri?cal solution of the stochastic heat equation with Neumann boundary conditions. For the proposed technique, the convergence criteria and the erro...
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| Veröffentlicht in: | Thermal science 2023, Vol.27 (Spec. issue 1), p.57-66 |
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| container_issue | Spec. issue 1 |
| container_start_page | 57 |
| container_title | Thermal science |
| container_volume | 27 |
| creator | Raja Balachandar, S. Uma, D. Jafari, H. Venkatesh, S.G. |
| description | In this article, we propose a new technique based on 2-D shifted Legendre
poly?nomials through the operational matrix integration method to find the
numeri?cal solution of the stochastic heat equation with Neumann boundary
conditions. For the proposed technique, the convergence criteria and the
error estima?tion are also discussed in detail. This new technique is tested
with two exam?ples, and it is observed that this method is very easy to
handle such problems as the initial and boundary conditions are taken care
of automatically. Also, the time complexity of the proposed approach is
discussed and it is proved to be O[k(N + 1)4] where N denotes the degree of
the approximate function and k is the number of simulations. This method is
very convenient and efficient for solving other partial differential
equations. |
| doi_str_mv | 10.2298/TSCI23S1057R |
| format | Article |
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poly?nomials through the operational matrix integration method to find the
numeri?cal solution of the stochastic heat equation with Neumann boundary
conditions. For the proposed technique, the convergence criteria and the
error estima?tion are also discussed in detail. This new technique is tested
with two exam?ples, and it is observed that this method is very easy to
handle such problems as the initial and boundary conditions are taken care
of automatically. Also, the time complexity of the proposed approach is
discussed and it is proved to be O[k(N + 1)4] where N denotes the degree of
the approximate function and k is the number of simulations. This method is
very convenient and efficient for solving other partial differential
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poly?nomials through the operational matrix integration method to find the
numeri?cal solution of the stochastic heat equation with Neumann boundary
conditions. For the proposed technique, the convergence criteria and the
error estima?tion are also discussed in detail. This new technique is tested
with two exam?ples, and it is observed that this method is very easy to
handle such problems as the initial and boundary conditions are taken care
of automatically. Also, the time complexity of the proposed approach is
discussed and it is proved to be O[k(N + 1)4] where N denotes the degree of
the approximate function and k is the number of simulations. This method is
very convenient and efficient for solving other partial differential
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poly?nomials through the operational matrix integration method to find the
numeri?cal solution of the stochastic heat equation with Neumann boundary
conditions. For the proposed technique, the convergence criteria and the
error estima?tion are also discussed in detail. This new technique is tested
with two exam?ples, and it is observed that this method is very easy to
handle such problems as the initial and boundary conditions are taken care
of automatically. Also, the time complexity of the proposed approach is
discussed and it is proved to be O[k(N + 1)4] where N denotes the degree of
the approximate function and k is the number of simulations. This method is
very convenient and efficient for solving other partial differential
equations.</abstract><doi>10.2298/TSCI23S1057R</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
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| ispartof | Thermal science, 2023, Vol.27 (Spec. issue 1), p.57-66 |
| issn | 0354-9836 2334-7163 |
| language | eng |
| recordid | cdi_crossref_primary_10_2298_TSCI23S1057R |
| source | Full-Text Journals in Chemistry (Open access); EZB Electronic Journals Library |
| title | Numerical solution for stochastic heat equation with Neumann boundary conditions |
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