Journal of Applied Mathematics and Computation

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Error Bounds for Krylov Approximation and Exact Solution of Identifying an Unknown Source in the Poisson Equation

Ousmane Samba Coulibaly1,*, Boureima Sangaré2

1Department of Mathematics, University of Science, Techniques and Technologies of Bamako (USTTB), Bamako, Mali.

2Department of Mathematics, University Nazi BONI, Bobo-Dioulasso, Houet, Burkina Faso.

*Corresponding author: Ousmane Samba Coulibaly

Published: May 6,2023


In this paper, we treat an ill-posed problem for the determination of an unknown source in the Poisson equation. We make a theoretical analysis of the approximation of the function  (A)g = (I −e −A) −1A2g by using the Krylov subspace me-thod, and we derive some error estimates. The idea is to project the approximate operator (I − e −A) −1A 2 on a small subspace, and perform matrix calculations that result. Having good estimates or even bounds for the error in computing approximations to expression of the f(A)v is very important in pratical application. This opportunity is for us to propose a basic approach to solving the inverse problem, then estimate the error to see its effectiveness and the convergence of the solution. This general approach, which has been used with success in several applications, provides a systematic way of defining high order explicit-type schemes for solving of Poisson equation.


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How to cite this paper

Error Bounds for Krylov Approximation and Exact Solution of Identifying an Unknown Source in the Poisson Equation

How to cite this paper: Ousmane Samba Coulibaly, Boureima Sangaré. (2023) Error Bounds for Krylov Approximation and Exact Solution of Identifying an Unknown Source in the Poisson EquationJournal of Applied Mathematics and Computation7(1), 188-201.