Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A NUMERICAL METHOD FOR CAUCHY PROBLEM USING SINGULAR VALUE DECOMPOSITION

  • Published : 2001.07.01
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Abstract

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of he domain, which provides the information on the choice of numerically meaningful modes. We suggest a pseudo-inverse regularization method based on singular value decomposition and present various numerical simulations.

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References

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