Solving the Cauchy problem for the Helmholtz equation using cubic smoothing splines

DOI10.1007/s12190-021-01572-3zbMath1491.35145OpenAlexW3167283790MaRDI QIDQ2142523

Fredrik Berntsson, Mary Nanfuka, John Magero Mango

Publication date: 27 May 2022

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-021-01572-3

zbMATH Keywords

Cauchy problemHelmholtz equationcubic splinesill-posed problem

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Related Items (1)

Determining radially symmetric potential from far-field scattering data

Cites Work

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• Error bounds for derivative estimates based on spline smoothing of exact or noisy data
• Two regularization methods for the Cauchy problems of the Helmholtz equation
• Variational methods for underwater acoustic problems
• The Fourier regularization for solving the Cauchy problem for the Helmholtz equation
• Two approximate methods of a Cauchy problem for the Helmholtz equation
• Regularization of the Cauchy problem for the Helmholtz equation by using Meyer wavelet
• A regularization method for a Cauchy problem of the Helmholtz equation
• Analysis of Dirichlet-Robin iterations for solving the Cauchy problem for elliptic equations
• The Detection of the Source of Acoustical Noise in Two Dimensions
• Robin–Dirichlet algorithms for the Cauchy problem for the Helmholtz equation
• Stability analysis of the Fourier–Bessel method for the Cauchy problem of the Helmholtz equation
• The detection of surface vibrations from interior acoustical pressure
• Numerical reconstruction of brain tumours
• Approximate solution of a Cauchy problem for the Helmholtz equation
• An alternating iterative procedure for the Cauchy problem for the Helmholtz equation
• SPLINE INTERPOLATION AND THE HIGHER DERIVATIVES
• Cubic B-spline method for the solution of an inverse parabolic system

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