A unified solution method for linear elliptic Cauchy problems
DOI10.1007/s40314-023-02267-0zbMath1524.65738OpenAlexW4324150119MaRDI QIDQ6044732
Mohsen Tadi, Miloje S. Radenkovic
Publication date: 22 May 2023
Published in: Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s40314-023-02267-0
Numerical optimization and variational techniques (65K10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A variational-type method of fundamental solutions for a Cauchy problem of Laplace's equation
- Moment theory and some inverse problems in potential theory and heat conduction
- The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation
- Meshless method based on the local weak-forms for steady-state heat conduction problems
- Solution of the Dirichlet and Neumann problems for a modified Helmholtz equation in Besov spaces on an annulus
- Solution of biharmonic equations with application to radar imaging
- Numerical solution of a non-classical two-phase Stefan problem via radial basis function (RBF) collocation methods
- New computational methods for inverse wave scattering with a new filtering technique. Inverse wave scattering
- Regularized solution of the Cauchy problem for the biharmonic equation
- The one-dimensional heat equation subject to a boundary integral specification
- BEM solution for the Cauchy problem associated with Helmholtz-type equations by the Landweber method
- Analytic extensions and Cauchy-type inverse problems on annular domains: stability results
- Definitions and examples of inverse and ill-posed problems
- A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s Equation
- An Introduction to Inverse Problems with Applications
- A local meshless procedure to determine the unknown control parameter in the multi-dimensional inverse problems
- An Energy Regularization for Cauchy Problems of Laplace Equation in Annulus Domain
- An introduction to the mathematical theory of inverse problems
This page was built for publication: A unified solution method for linear elliptic Cauchy problems
