Regularization and Error Estimate for the Poisson Equation with Discrete Data
Keyword(s):
In this work, we focus on the Cauchy problem for the Poisson equation in the two dimensional domain, where the initial data is disturbed by random noise. In general, the problem is severely ill-posed in the sense of Hadamard, i.e., the solution does not depend continuously on the data. To regularize the instable solution of the problem, we have applied a nonparametric regression associated with the truncation method. Eventually, a numerical example has been carried out, the result shows that our regularization method is converged; and the error has been enhanced once the number of observation points is increased.
2021 ◽
Vol 18
(03)
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pp. 701-728
2019 ◽
Vol 39
(11)
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pp. 6713-6745
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Keyword(s):
Keyword(s):
2019 ◽
Vol 17
(05)
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pp. 1950029
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Keyword(s):
2020 ◽