An iterative method for cauchy problems subject to the convection-diffusion equation

In this text, we presented the Nachaoui’s iterative alternating method for solving the Cauchy problemgoverned by the convection-diffusion equation. The method is an iterative algorithm that alternates betweensolving two subproblems of the same type with boundary conditions of the Dirichlet and Neuma...

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Bibliographic Details
Published inAdvanced mathematical models & applications Vol. 8; pp. 327 - 338
Main Author Nachaoui, Abdeljalil
Format Journal Article
LanguageEnglish
Published Jomard Publishing 30.11.2023
Subjects
Mathematics
Convection-diffusion equations
Ill-posed problems
Inverse problems
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Summary:In this text, we presented the Nachaoui’s iterative alternating method for solving the Cauchy problemgoverned by the convection-diffusion equation. The method is an iterative algorithm that alternates betweensolving two subproblems of the same type with boundary conditions of the Dirichlet and Neuman type on theinaccessible part of the boundary. The algorithm continues iterating until a convergence criterion is met. Wediscussed the convergence and computational efficiency of the method. The numerical results show that themethod is computationally efficient and that the relaxation parameter can greatly reduce the number ofiterations.
ISSN:2519-4445
2519-4445