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Fourth-order modified method for the Cauchy problem for the Laplace equation. (English) Zbl 1093.65107
A Cauchy problem for the Laplace equation in a strip is presented. The equation is modified by adding a fourth order mixed derivative with a coefficient that serves as a regularization parameter. It is shown that for a certain choice of the parameter the error estimate is of almost Hölders type. Numerical experiments are performed for illustration.

65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35R25 Ill-posed problems for PDEs
Full Text: DOI
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