Exact error estimation for solutions of nuclide chain equations

The exact solution of nuclide chain equations within arbitrary figures is o btained fur a linear chain by employing the Bateman method in the multiple- precision arithmetic. The exact error estimation of major calculation metho ds for a nuclide chain equation is done by using this exact solution as a s tandard, The Bateman. finite difference. Runge-Kutta and matrix exponential methods are investigated. The present study confirms the following. The original Bateman method has v ery low accuracy in some cases, because of large-scale cancellations. The r evised Bateman method by Siewers reduces the occurrence of cancellations an d thereby shows high accuracy In the time difference method as the finite d ifference 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 accu mulation of round-off errors, it appears to be nonpractical. Judging from t hese estimations, the matrix exponential method is the best among all the m ethods except the Bateman method whose calculation process for a linear cha in is not identical with that for a general one.