Generalized Tikhonov Method and Convergence Estimate for the Cauchy Problem of Modified Helmholtz Equation with Nonhomogeneous Dirichlet and Neumann Datum
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A Priori
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We investigate a Cauchy problem of the modified Helmholtz equation with nonhomogeneous Dirichlet and Neumann datum, this problem is ill-posed and some regularization techniques are required to stabilize numerical computation. We established the result of conditional stability under an a priori assumption for an exact solution. A generalized Tikhonov method is proposed to solve this problem, we select the regularization parameter by a priori and a posteriori rules and derive the convergence results of sharp type for this method. The corresponding numerical experiments are implemented to verify that our regularization method is practicable and satisfied.
2012 ◽
Vol 2012
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pp. 1-13
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2014 ◽
Vol 38
(17)
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pp. 3711-3719
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2011 ◽
Vol 28
(3)
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pp. 899-925
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2010 ◽
Vol 45
(6)
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pp. 665-677
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2009 ◽
Vol 2
(3)
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pp. 326-340
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