Runge-Kutta methods for stochastic differential equations

我们考虑了带噪声项的常微分方程的数值方法。一般来说，这样的方法需要大量的（伪）随机数和大量的方程中的扩散系数的评估。在本研究课题中，提出了高精度的数值格式，其中两个数字之和小于现有的计划需要。顺便提及，因为数值计算会引起数值误差，所以希望采用受误差影响较小的方法。这种高精度的方法也已被提出。

We have considered numerical methods for ordinary differential equations with noise terms. In general, such methods need a large number of (pseudo-) random numbers and a large number of evaluations of the diffusion coefficients in the equations. In this research subject, numerical schemes with high precision have been proposed in which the sum of the both numbers is smaller than existing schemes need. Incidentally, because numerical calculations cause numerical errors, methods less influenced by the errors are desirable. Such methods with high precision have been also proposed.