Numerical Method for Backward Heat Conduction Problems Using an Arbitrary-Order Finite Difference Method

Iijima, Kentaro

doi:10.1016/b978-008044268-6/50010-7

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“…One may refer to Iijima [3] for the case that P (∂) is the heat operator ∂/∂t − ∆. Corresponding to the operator P (∂), we consider the µ-th order polynomial…”

Section: High Order Finite Difference Methodsmentioning

confidence: 99%

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A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

Saito

Nakada

Iijima

et al. 2005

J. Phys.: Conf. Ser.

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Abstract. Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr. Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

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“…One may refer to Iijima [3] for the case that P (∂) is the heat operator ∂/∂t − ∆. Corresponding to the operator P (∂), we consider the µ-th order polynomial…”

Section: High Order Finite Difference Methodsmentioning

confidence: 99%

“…To solve this problem numerically, we apply a quasi-spectral method [2] consisting of a high order finite difference method [3], [4] to its approximation. The conventional finite difference method approximates unknown derivatives, based on some polynomials [5], [6].…”

Section: High Order Finite Difference Methodsmentioning

confidence: 99%