×

Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation. (English) Zbl 0980.35167

Summary: The highly ill-posed Cauchy problem for the Laplace equation is transformed to a classical moment problem whose numerical approximation can be achieved. Proofs on its convergence and stability estimates are given based on the Backus-Gilbert algorithm. For numerical verification, several examples which include random noise in the initial Cauchy data are presented.

MSC:

35R25 Ill-posed problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
PDFBibTeX XMLCite
Full Text: DOI Link