On the Chandrasekhar integral equation
[EN] This study is devoted to solve the Chandrasekhar integral equation that it is used for modeling problems in theory of radiative transfer in a plane-parallel atmosphere, and others research areas like the kinetic theory of gases, neutron transport, traffic model, the queuing theory among others....
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2021 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositório: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglês |
| OAI Identifier: | oai:riunet.upv.es:10251/181810 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/181810 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Convergence order Domain of existence of solution Domain of uniqueness of solution Integral equation Newton iterative scheme Nonlinear equation Nonseparable kernel MATEMATICA APLICADA |
| Resumo: | [EN] This study is devoted to solve the Chandrasekhar integral equation that it is used for modeling problems in theory of radiative transfer in a plane-parallel atmosphere, and others research areas like the kinetic theory of gases, neutron transport, traffic model, the queuing theory among others. First of all, we transform the Chandrasekhar integral equation into a nonlinear Hammerstein-type integral equation with the corresponding Nemystkii operator and the proper nonseparable kernel. Them, we approximate the kernel in order to apply an iterative scheme. This procedure it is solved in two different ways. First one, we solve a nonlinear equation with separable kernel and define an adequate nonlinear operator between Banach spaces that approximates the first problem. Second one, we introduce an approximation for the inverse of the Frechet derivative that appears in the Newton's iterative scheme for solving nonlinear equations. Finally, we perform a numerical experiment in order to compare our results with previous ones published showing that are competitive. |
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