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11 papers · 1 filter
Improvement of Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind and their theoretical analysis
Tomoaki Okayama
Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind were proposed independently by multiple authors: by Shamloo et al. in 2012 and by Mesgarani and…
Error analyses of Sinc-collocation methods for exponential decay initial value problems
Tomoaki Okayama, Ryota Hara, Shun'ichi Goto
Nurmuhammad et al. developed the Sinc-Nyström methods for initial value problems in which the solutions exhibit exponential decay end behavior. In these methods, the Single-Exponen…
Improvement of selection formulas of mesh size and truncation numbers for the DE-Sinc approximation and its theoretical error bound
Tomoaki Okayama, Shota Ogawa
The Sinc approximation applied to double-exponentially decaying functions is referred to as the DE-Sinc approximation. Because of its high efficiency, this method has been used in…
New conformal map for the trapezoidal formula for infinite integrals of unilateral rapidly decreasing functions
Tomoaki Okayama, Tomoki Nomura, Saki Tsuruta
While the trapezoidal formula can attain exponential convergence when applied to infinite integrals of bilateral rapidly decreasing functions, it is not capable of this in the case…
New conformal map for the Sinc approximation for exponentially decaying functions over the semi-infinite interval
Tomoaki Okayama, Yuya Shintaku, Eisuke Katsuura
The Sinc approximation has shown high efficiency for numerical methods in many fields. Conformal maps play an important role in the success, i.e., appropriate conformal map must be…
An optimal approximation formula for functions with singularities
Ken'ichiro Tanaka, Tomoaki Okayama, Masaaki Sugihara
We propose an optimal approximation formula for analytic functions that are defined on a complex region containing the real interval and possibly have algebraic singularit…