摘要
求解随机微分方程时,为了更好地使数值解逼近解析解,文章将平衡法与θ-Heun法结合构成平衡θ-Heun法。当控制参数确定时,对于带有乘性噪音的随机微分方程,给出了平衡θ-Heun法均方稳定的条件,并证明了平衡θ-Heun法的指数稳定性。最后的数值算例给出了相关结论的验证,比较了3种Heun方法的稳定性。
When solving stochastic differential equations,in order to better approximate the numerical solution to the analytical solution,the balancedθ-Heun method was obtained by combining the balance method andθ-Heun method.For a stochastic differential equation with multiplicative noise,as the control parameters were determined,the conditions of the mean square stability for the balancedθ-Heun method were given and the exponential stability of the balancedθ-Heun method was proved.Finally,the numerical example was given to verify theoretical results and the stability of three Heun methods was compared.
作者
康红喜
张引娣
蒋茜
KANG Hongxi;ZHANG Yindi;JIANG Qian(School of Science, Chang’an University, Xi’an 710064, China)
出处
《合肥工业大学学报（自然科学版）》
CAS
北大核心
2021年第2期284-288,共5页
Journal of Hefei University of Technology：Natural Science
基金
国家自然科学基金资助项目(11572146)。
关键词
随机微分方程
平衡θ-Heun法
均方稳定性
指数稳定性
stochastic differential equation
balancedθ-Heun method
mean square stability
exponential stability
