Numerical Solution to the Cauchy Problem of the Laplace Equation with Noisy Data
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Our particular interest is a numerical treatment of noisy data for ill-posed problems of partial differential equations. Our method consists of the multiple-precision arithmetic system exflib developed by Dr. Fujiwara of Kyoto University for numerical computation and the high order finite difference method developed by Iijima for approximation of differential equations. In this paper, this combined method is applied to numerical solution to the Cauchy problem of the Laplace equation. A rank reduction technique is considered for regularization to the problem with noisy data.
- Theoretical and Applied Mechanics Japan
Theoretical and Applied Mechanics Japan 57(0), 481-486, 2009
National Committee for IUTAM