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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Bibliographic Details
Main Authors:	Olivar Robayo, Luis Eduardo, Granada Díaz, Héctor Andrés
Format:	Online
Published:	Universidad Pedagógica y Tecnológica de Colombia 2024
Subjects:	Problemas inversos, métodos de regularización, ecuaciones elípticas, problemas mal puestos, métodos de molificación Inverse problems, regularization methods, elliptic equations, ill-posed problems, mollification methods.
Online Access:	https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/16629

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Summary:	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.