Recursive Formula for the Trial Function Boundary Function
The neural network trial function method of Legaris et al. (Artificial neural networks for solving ordinary and partial differential equations, IEEE Trans. Neural Netw. 9(5) (1998) 987–1000) requires the specification of a boundary function that matches the boundary values and is finite in the solut...
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| Language: | English |
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World Scientific Publishing
2025-01-01
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| Series: | Computing Open |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S2972370125500023 |
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| author | E. L. Winter R. S. Weigel |
| author_facet | E. L. Winter R. S. Weigel |
| author_sort | E. L. Winter |
| collection | DOAJ |
| description | The neural network trial function method of Legaris et al. (Artificial neural networks for solving ordinary and partial differential equations, IEEE Trans. Neural Netw. 9(5) (1998) 987–1000) requires the specification of a boundary function that matches the boundary values and is finite in the solution domain. We develop a recursive formula for generating a boundary function for up to second-order partial differential equations with Dirichlet boundary conditions in a finite hyper-box domain and with an arbitrary number of dimensions. |
| format | Article |
| id | doaj-art-4615fdb6a7aa40d9b5387fe4381f5cdb |
| institution | OA Journals |
| issn | 2972-3701 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Computing Open |
| spelling | doaj-art-4615fdb6a7aa40d9b5387fe4381f5cdb2025-08-20T01:55:10ZengWorld Scientific PublishingComputing Open2972-37012025-01-010310.1142/S2972370125500023Recursive Formula for the Trial Function Boundary FunctionE. L. Winter0R. S. Weigel1Applied Physics Lab, Johns Hopkins University, 7651 Montpelier Road, Laurel, MD 20723, USADepartment of Physics and Astronomy, George Mason University, 4400 University Drive, Fairfax, VA 22030, USAThe neural network trial function method of Legaris et al. (Artificial neural networks for solving ordinary and partial differential equations, IEEE Trans. Neural Netw. 9(5) (1998) 987–1000) requires the specification of a boundary function that matches the boundary values and is finite in the solution domain. We develop a recursive formula for generating a boundary function for up to second-order partial differential equations with Dirichlet boundary conditions in a finite hyper-box domain and with an arbitrary number of dimensions.https://www.worldscientific.com/doi/10.1142/S2972370125500023Differential equationspartial differential equationsneural networksboundary valuetrial function |
| spellingShingle | E. L. Winter R. S. Weigel Recursive Formula for the Trial Function Boundary Function Computing Open Differential equations partial differential equations neural networks boundary value trial function |
| title | Recursive Formula for the Trial Function Boundary Function |
| title_full | Recursive Formula for the Trial Function Boundary Function |
| title_fullStr | Recursive Formula for the Trial Function Boundary Function |
| title_full_unstemmed | Recursive Formula for the Trial Function Boundary Function |
| title_short | Recursive Formula for the Trial Function Boundary Function |
| title_sort | recursive formula for the trial function boundary function |
| topic | Differential equations partial differential equations neural networks boundary value trial function |
| url | https://www.worldscientific.com/doi/10.1142/S2972370125500023 |
| work_keys_str_mv | AT elwinter recursiveformulaforthetrialfunctionboundaryfunction AT rsweigel recursiveformulaforthetrialfunctionboundaryfunction |