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- W2019332422 abstract "In this paper we derive a formula for indefinite integration of analytic functions over (−1, s ) where −1< s <1, by means of the double exponential transformation and the Sinc method. The integrand must be analytic on −1< x <1 but may have a singularity at the end points x =±1. The error of the formula behaves approximately as exp (−c 1 N/ log c 2 N) where N is the number of function evaluations of the integrand. This error term shows a much faster convergence to zero when N becomes large than that of the known formula by Haber. Also we derive efficient double exponential formulas for numerical evaluation of indefinite integrals over (0, s ), 0< s <∞ and over (−∞, s ), −∞< s <+∞. Several numerical examples indicate high efficiency of the formulas." @default.
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- W2019332422 date "2003-12-01" @default.
- W2019332422 modified "2023-09-29" @default.
- W2019332422 title "Double exponential formulas for numerical indefinite integration" @default.
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- W2019332422 doi "https://doi.org/10.1016/j.cam.2003.05.002" @default.
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