随机微分方程组的依方程变步长Euler方法  

Euler methods with different step-sizes for different equations for stochastic differential equations

作　　者：范振成[1] 肖宇[2] 

机构地区：[1]闽江学院数学系,福州350108 [2]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2013年第3期335-340,共6页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11101199);福建省自然科学基金资助项目(2011J01016);福建省教育厅科研资助项目(JA11204)

摘　　要：以二维随机微分方程的初值问题为例,考虑随机多重速率问题的数值解法。通过对方程组的不同方程交替使用不同步长的Euler方法,建立依方程变步长的数值方法。将数值迭代公式连续化,得到描述近似解误差的关系式,然后利用Gronwall不等式估计误差。结果表明:数值计算方法是收敛的。数值实验说明:对多重速率问题,此方法比传统的固定步长Euler方法效率更高。Consider the numerical methods of the stochastic multi-rate question by studying the initial value problem of the two-dimensional stochastic differential equations. The numerical method with the different step-sizes for the different equations is proposed, where the Euler methods with different step-size, in turn, are used for different equations. By using the continuous version of the numerical method, the formula describing the error of the approxi- mate solution is obtained, and then the error is estimated by the Gronwall inequality, which shows that the numerical method is convergent. Finally, the numerical experiment shows that the new method is more efficient than the Euler methods with uniform step-size for the multi-rate question.

关 键 词：随机微分方程 EULER方法 变步长 

分 类 号：O211.63[理学—概率论与数理统计]