553 Numerical Analysis of the Three-Dimensional Cavity Flow Using Higher-Degree Interpolation Scheme

Akimoto, Tomohiro; Tosaka, Nobuyoshi

doi:10.1299/jsmecmd.2001.14.639

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The conventional finite difference method approximates unknown derivatives, based on some polynomials [5], [6]. Some other recent methods [7], [8], [9] are worthy of note in this connection on polynomials. On the other hand, our high order finite difference method approximates unknown derivatives, based on exponential functions.…”

Section: High Order Finite Difference Methodsmentioning

confidence: 99%

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.

View full text Add to dashboard Cite

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.

show abstract

Section: High Order Finite Difference Methodsmentioning

confidence: 99%