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Journals and Conferences
A method, called " the discrete variational method " , has been recently presented by Furihata and Matsuo for designing finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations (PDEs). In this paper the method is enhanced so that the derived schemes be highly accurate in space by… (More)
We will give a summary about the relations between the spectra of the Perron–Frobenius operator and pseudo random sequences for 1-dimensional cases. There are many difficulties to construct general theory of higher-dimensional cases. We will give several examples for these cases.
This paper deals with a finite element method involving Petrov-Galerkin method with cubic B-splines as basis functions and quintic B-splines as weight functions to solve a general fourth order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary… (More)
The double exponential formula, abbreviated as the DE-formula, was first presented by Takahasi and Mori  in 1974 as an efficient and robust quadrature formula to compute integrals with end point singularity, e.g. 1 = L (X-2)(1-X)V4(1+J03/4 > C 1) or over the half infinite interval, e.g.-/ Jo OO e~*logxsinxdx. (2) The DE-formula is based on the… (More)
μ Γ(z) = √ 2π(z + μ) z−1/2 e −z−μ A μ (z), A μ (z) = c 0 + c 1 z − 1 z + c 2 (z − 1)(z − 2) z(z + 1) + c 3 (z − 1)(z − 2)(z − 3) z(z + 1)(z + 2) + · · · (1) c n n j=0 2n n − j c j = (2n)! n! e n+1+μ √ 2π(n + 1 + μ) n+1/2 , n = 0, 1, 2,. . .