Application of the Two-sided difference quotient in the solution of nonlinear Ill-posed inverse self-adjoint elliptic problem
When we use a discretization by finite differences, to solve differential equations we find problems at the border of the domain of the solution. If the solution is also immersed in a ill-posed inverse problem; we can find very bad solutions. In this paper we apply a discretization of two - sided di...
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| Format: | Online |
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Universidad Pedagógica y Tecnológica de Colombia
2024
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| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/16629 |
| _version_ | 1801706360574836736 |
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| author | Olivar Robayo, Luis Eduardo Granada Díaz, Héctor Andrés |
| author_facet | Olivar Robayo, Luis Eduardo Granada Díaz, Héctor Andrés |
| author_sort | Olivar Robayo, Luis Eduardo |
| collection | OJS |
| description | When we use a discretization by finite differences, to solve differential equations we find problems at the border of the domain of the solution. If the solution is also immersed in a ill-posed inverse problem; we can find very bad solutions. In this paper we apply a discretization of two - sided difference quotients method to solve Ill-posed inverse self-adjoint elliptic problem [Kirsch(2011)]. Some numerical examples showing the effectiveness of this method and we will use mollification techniques to smooth the solutions. |
| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-16629 |
| institution | Revista Ciencia en Desarrollo |
| publishDate | 2024 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-166292024-05-11T07:16:52Z Application of the Two-sided difference quotient in the solution of nonlinear Ill-posed inverse self-adjoint elliptic problem Aplicación de un método de cociente de diferencias de dos lados en la solución de un problema inverso mal puesto no lineal de una ecuación elíptica auto-adjunta Olivar Robayo, Luis Eduardo Granada Díaz, Héctor Andrés Problemas inversos, métodos de regularización, ecuaciones elípticas, problemas mal puestos, métodos de molificación Inverse problems, regularization methods, elliptic equations, ill-posed problems, mollification methods. When we use a discretization by finite differences, to solve differential equations we find problems at the border of the domain of the solution. If the solution is also immersed in a ill-posed inverse problem; we can find very bad solutions. In this paper we apply a discretization of two - sided difference quotients method to solve Ill-posed inverse self-adjoint elliptic problem [Kirsch(2011)]. Some numerical examples showing the effectiveness of this method and we will use mollification techniques to smooth the solutions. Cuando utilizamos una discretización por diferencias finitas para solucionar ecuaciones diferenciales, encontramos problemas en la frontera del dominio de la solución; si además la solución esta inmersa en un problema inverso mal puesto, podemos encontrar soluciones muy malas. En este artículo aplicamos una discretización del cociente de diferencias de dos lados para resolver un problema elíptico autoadjunto inverso mal puesto [Kirsch(2011)]. Mostraremos algunos ejemplos numéricos que muestran la efectividad de este método y usaremos técnicas de molificación para suavizar las soluciones. Universidad Pedagógica y Tecnológica de Colombia 2024-04-09 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/16629 10.19053/01217488.v15.n1.2024.16629 Ciencia En Desarrollo; Vol. 15 No. 1 (2024): Vol 15, Núm.1 (2024): Enero-Junio Ciencia en Desarrollo; Vol. 15 Núm. 1 (2024): Vol 15, Núm.1 (2024): Enero-Junio 2462-7658 0121-7488 |
| spellingShingle | Problemas inversos, métodos de regularización, ecuaciones elípticas, problemas mal puestos, métodos de molificación Inverse problems, regularization methods, elliptic equations, ill-posed problems, mollification methods. Olivar Robayo, Luis Eduardo Granada Díaz, Héctor Andrés Application of the Two-sided difference quotient in the solution of nonlinear Ill-posed inverse self-adjoint elliptic problem |
| title | Application of the Two-sided difference quotient in the solution of nonlinear Ill-posed inverse self-adjoint elliptic problem |
| title_alt | Aplicación de un método de cociente de diferencias de dos lados en la solución de un problema inverso mal puesto no lineal de una ecuación elíptica auto-adjunta |
| title_full | Application of the Two-sided difference quotient in the solution of nonlinear Ill-posed inverse self-adjoint elliptic problem |
| title_fullStr | Application of the Two-sided difference quotient in the solution of nonlinear Ill-posed inverse self-adjoint elliptic problem |
| title_full_unstemmed | Application of the Two-sided difference quotient in the solution of nonlinear Ill-posed inverse self-adjoint elliptic problem |
| title_short | Application of the Two-sided difference quotient in the solution of nonlinear Ill-posed inverse self-adjoint elliptic problem |
| title_sort | application of the two sided difference quotient in the solution of nonlinear ill posed inverse self adjoint elliptic problem |
| topic | Problemas inversos, métodos de regularización, ecuaciones elípticas, problemas mal puestos, métodos de molificación Inverse problems, regularization methods, elliptic equations, ill-posed problems, mollification methods. |
| topic_facet | Problemas inversos, métodos de regularización, ecuaciones elípticas, problemas mal puestos, métodos de molificación Inverse problems, regularization methods, elliptic equations, ill-posed problems, mollification methods. |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/16629 |
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