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- W4243989898 abstract "The exact solution of nuclide chain equations within arbitrary figures is obtained for a linear chain by employing the Bateman method in the multiple-precision arithmetic. The exact error estimation of major calculation methods for a nuclide chain equation is done by using this exact solution as a standard. The Bateman, finite difference, Runge-Kutta and matrix exponential methods are investigated.The present study confirms the following. The original Bateman method has very low accuracy in some cases, because of large-scale cancellations. The revised Bateman method by Siewers reduces the occurrence of cancellations and thereby shows high accuracy. In the time difference method as the finite difference and Runge-Kutta methods, the solutions are mainly affected by the truncation errors in the early decay time, and afterward by the round-off errors. Even though the variable time mesh is employed to suppress the accumulation of round-off errors, it appears to be nonpractical. Judging from these estimations, the matrix exponential method is the best among all the methods except the Bateman method whose calculation process for a linear chain is not identical with that for a general one." @default.
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- W4243989898 date "1999-01-01" @default.
- W4243989898 modified "2023-09-27" @default.
- W4243989898 title "Exact Error Estimation for Solutions of Nuclide Chain Equations." @default.
- W4243989898 doi "https://doi.org/10.3327/jnst.36.1176" @default.
- W4243989898 hasPublicationYear "1999" @default.
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