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Solving the Cauchy ...
Solving the Cauchy problem for the Helmholtz equation using cubic smoothing splines
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- Nanfuka, Mary (författare)
- Mbarara Univ Sci & Technol, Uganda; Makerere Univ, Uganda
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- Berntsson, Fredrik (författare)
- Linköpings universitet,Tillämpad matematik,Tekniska fakulteten
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- Mango, John (författare)
- Makerere Univ, Uganda
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(creator_code:org_t)
- 2021-06-11
- 2022
- Engelska.
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Ingår i: Journal of Applied Mathematics and Computing. - : Springer Berlin/Heidelberg. - 1598-5865 .- 1865-2085. ; 68:2, s. 1335-1350
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Abstract
Ämnesord
Stäng
- We consider the Cauchy problem for the Helmholtz equation defined in a rectangular domain. The Cauchy data are prescribed on a part of the boundary and the aim is to find the solution in the entire domain. The problem occurs in applications related to acoustics and is illposed in the sense of Hadamard. In our work we consider regularizing the problem by introducing a bounded approximation of the second derivative by using Cubic smoothing splines. We derive a bound for the approximate derivative and show how to obtain stability estimates for the method. Numerical tests show that the method works well and can produce accurate results. We also demonstrate that the method can be extended to more complicated domains.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Helmholtz equation; Cauchy Problem; Illposed; Cubic Splines
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