求解初值问题的仿真算法和人工舍入误差的应用

ON SIMULATION ALGORITHMS FOR INITIAL VALUE PROBLEMS AND APPLICATION OF ARTIFICIAL ROUND - OFF ERROR

求解初值问题的仿真算法和人工舍入误差的应用李旺尧（中科院计算数学与科学工程计算所）ＯＮＳＩＭＵＬＡＴＩＯＮＡＬＧＯＲＩＴＨＭＳＦＯＲＩＮＩＴＩＡＬＶＡＬＵＥＰＲＯＢＬＥＭＳＡＮＤＡＰＰＬＩＣＡＴＩＯＮＯＦＡＲＴＩＦＩＣＩＡＬＲＯＵＮＤ－ＯＦＦＥＲＲＯ...

Abstract The simulation algoritluns are advanced in this paper.The simulation algorithms are constructed by a series of step equivalent phasenow operator' The step equivalent phase flow operator produces the almost same numerical result as the phase flow operator dose in computer system.Therefore the numerical solution of simulation algorithms can reflect all featuresof the true solution of differential equation and the simulation algorithms areuniversally suitable for initial value problems of ordinary differential equation, especially for those which possess obvious construct features.The step equivalent phase flow operator can be constructed by almost alltraditional algorithms, so we have very extensive choice for getting simulationalgorithms. Explicit methods with higher order may be chosen to decrease the amountof calculation and to increase the integration step size.Some typical Hamiltonian systems are solved and the numerical tests supportabove mentioned conclusions.Under given conditions the traditional algorithms change into simulationalgorithms due to round -off operation of computer, but the artificial round -off operation can also play the same role.A simple method of artificial round-off is present in this paper and the numericaltests show that it is available.