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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.

MSC:
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
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