Abstract

OLIVAR ROBAYO, Luis Eduardo  and  GRANADA DIAZ, Hector Andres. Application of the Two-sided difference quotient in the solution of nonlinear Ill-posed. Ciencia en Desarrollo [online]. 2024, vol.15, n.1, pp.150-154.  Epub Oct 15, 2024. ISSN 0121-7488.  https://doi.org/10.19053/01217488.v15.n1.2024.16629.

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 [1]. Some numerical examples showing the effectiveness of this method and we will use mollification techniques to smooth the solutions.

Keywords : Inverse problems; regularization methods; elliptic equations; ill-posed problems; mollification methods.

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