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- W2086344685 abstract "Abstract In the numerical calculation of f(t ), the inverse Laplace transform of F ( p ), where f (′) = (1/2 πi ) ° c − i ∞ c + i ∞ e pt F ( p ) dp , sufficient accuracy is usually obtainable when p 3 F ( p ), s > 0, is replaced by an interpolating polynomial in 1/ p . From the values of F ( p ) with F ′( p ), or with F ′( p ) and F ″( p ), for p at points equally spaced on the real axis, an osculatory or hyperosculatory interpolation polynomial for p 8 F ( p ), namely L 2 n −1 ( x ) or L 3 n −1 ( x ), where x = 1/ p , is obtained in barycentric form. Then f(t) is calculated by a Gaussian-type quadrature formula employing complex values of L 2 n −1 or L 3 n −1 and instead of p s F ( p ) which may be unknown or more difficult to compute. For calculating L 2 n −1 and L 3 n −1 , auxiliary coefficients, suitable for economical storage in the program, are given exactly for n = 2(1)11 and n = 2(1)7, furnishing up to 21st and 20th degree accuracy, respectively." @default.
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- W2086344685 date "1975-04-01" @default.
- W2086344685 modified "2023-09-23" @default.
- W2086344685 title "Note on laplace transforms of osculatory and hyperosculatory interpolation polynomials" @default.
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- W2086344685 doi "https://doi.org/10.1016/0021-9991(75)90044-3" @default.
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