Polynomial approximation of an inverse Cauchy problem for Helmholtz type equations

The objective of this paper is to solve numerically a Cauchy problem defined on a two-dimensional domain occupied by a material satisfying the Helmholtz type equations and verifying additional Cauchy-type boundary conditions on the accessible part of the boundary. A meshless numerical method using a...

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Bibliographic Details
Published inAdvanced mathematical models & applications Vol. 7; no. 3; pp. 306 - 322
Main Authors Aboud, Fatima, Jameel, Ibtihal Th, Hasan, Athraa F., Mostafa, Baydaa Kh, Nachaoui, Abdeljalil
Format Journal Article
LanguageEnglish
Published Jomard Publishing 16.12.2022
Subjects
Mathematics
Numerical Analysis
Helmholtz equation
Helmholtz equation inverse Cauchy Problem meshless method CG CGLS AMS Subject Classification: 65N21 41A10 65F22 65N35
Inverse Cauchy Problem
CG
CGLS
Meshless method
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Summary:The objective of this paper is to solve numerically a Cauchy problem defined on a two-dimensional domain occupied by a material satisfying the Helmholtz type equations and verifying additional Cauchy-type boundary conditions on the accessible part of the boundary. A meshless numerical method using an approximation of the solution based on the polynomial expansion is applied. To confirm the efficiency of the proposed method, different examples were considered and the obtained linear system was solved using the well-known CG and CGLS algorithms.
ISSN:2519-4445
2519-4445