探讨蒙特卡罗方法在解微分方程边值问题中的应用

On the Application of Monte Carlo Method in Solving the Problem of Boundary Value of Differential Equation

蒙特·卡罗方法 (Monte Carlo method),也称统计模拟方法,简写MC。是由20世纪40年代美国在第二次世界大战中研制原子弹的"曼哈顿计划"中的计划成员S.M.乌拉姆和J.冯·诺伊曼首先提出。之后数学家将其命名为蒙特卡罗,它以概率理论为指导,是一种非常重要的统计方法,利用常见的伪随机数解决多种计算问题的方法。这种方法在金融工程学、宏观经济学、计算物理学等领域被广泛的应用。早在18世纪法国数学家布丰利用投针实验的方法求圆周率π,被认为是蒙特·卡罗方法的起源。

Monte Carlo Method, abbreviated as MC, is also called statistical simulation method. It was first put forward in 1940 s by S. M. Ulam and J. V. Neumann, participants of the ＂Manhattan Project＂ which aimed at the development of atomic bomb in the World II. Later, mathematicians named it Monte Carlo Method. It is a very important statistical method which, under the guidance of probability theory, is used to solve various computing problems by means of pseudo-random numbers and it is widely used in the fields of financial engineering, macro-economics, computational physics, etc. In the 18 th century, Buffon, a French mathematician,used the needle-test method to calculateπ, the PI, which is considered the beginning of applying Monte Carlo Method.