11 citations · 39 across the 17 of their papers we have counts for
19 papers
DE-Sinc approximation for unilateral rapidly decreasing functions and its computable error bound
Tomoaki Okayama
The Sinc approximation is highly effective for functions that decay rapidly at both ends of the real axis. For unilateral rapidly decreasing functions, which decay algebraically as…
Refinement of the theory and convergence of the Sinc convolution -- beyond Stenger's conjecture
Tomoaki Okayama
The Sinc convolution is an approximate formula for indefinite convolutions proposed by Stenger. The formula was derived based on the Sinc indefinite integration formula combined wi…
Improvement of conformal maps combined with the Sinc approximation for derivatives over infinite intervals
Tomoaki Okayama, Yuito Kuwashita, Ao Kondo
F. Stenger proposed efficient approximation formulas for derivatives over infinite intervals. These formulas were derived by combining the Sinc approximation with appropriate confo…
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…
Relation between two Sinc-collocation methods for Volterra integral equations of the second kind and further improvement
Tomoaki Okayama
Stenger and Rashidinia--Zarebnia independently proposed two Sinc-collocation methods for Volterra integral equations of the second kind, but the relation between the methods has no…
Explicit error bounds of the SE and DE formulas for integrals with logarithmic and algebraic singularity
Tomoaki Okayama, Kosei Arakawa, Ryo Kamigaki +1
The single exponential (SE) and double exponential (DE) formulas are widely recognized as efficient quadrature formulas for evaluating integrals with endpoint singularity. For inte…
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…
Sinc-collocation methods with consistent collocation points for Fredholm integral equations of the second kind
Tomoaki Okayama
Sinc-collocation methods are known to be efficient for Fredholm integral equations of the second kind, even if functions in the equations have endpoint singularity. However, existi…
Yet another DE-Sinc indefinite integration formula
Tomoaki Okayama, Ken'ichiro Tanaka
Based on the Sinc approximation combined with the tanh transformation, Haber derived an approximation formula for numerical indefinite integration over the finite interval (-1, 1).…
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…
Error estimates with explicit constants for the Sinc approximation over infinite intervals
Tomoaki Okayama
The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functi…
Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces
Ken'ichiro Tanaka, Tomoaki Okayama, Masaaki Sugihara
We propose a method for designing accurate interpolation formulas on the real axis for the purpose of function approximation in weighted Hardy spaces. In particular, we consider th…
Theoretical analysis of a Sinc-Nyström method for Volterra integro-differential equations and its improvement
Tomoaki Okayama
A Sinc-Nyström method for Volterra integro-differential equations was developed by Zarebnia in 2010. The method is quite efficient in the sense that exponential convergence can be…
Explicit error bound for modified numerical iterated integration by means of Sinc methods
Tomoaki Okayama
This paper reinforces numerical iterated integration developed by Muhammad--Mori in the following two points: 1) the approximation formula is modified so that it can achieve a bett…
Theoretical analysis of Sinc-collocation methods and Sinc-Nyström methods for initial value problems
Tomoaki Okayama
A Sinc-collocation method has been proposed by Stenger, and he also gave theoretical analysis of the method in the case of a `scalar' equation. This paper extends the theoretical r…
Error Estimates with Explicit Constants for Sinc Quadrature and Sinc Indefinite Integration over Infinite Intervals
Tomoaki Okayama
The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any in…