变分数阶非线性随机微积分方程的Euler-Maruyama方法  

EULER-MARUYAMA METHOD FOR A CLASS OF VARIABLE-ORDER FRACTIONAL NONLINEAR STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS

作　　者：吕静云 张静娜 郑雨 Lv Jingyun;Zhang Jingna;Zheng Yu(School of Fundamental Education,Beijing Polytechnic College,Beijing 100042,China;LSEC,ICMSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;School of Mathematical Sciences,Yangzhou University,Yangzhou 225009,China)

机构地区：[1]北京工业职业技术学院基础教育学院,北京100042 [2]LSEC,ICMSEC,中国科学院数学与系统科学研究院,北京100190 [3]中国科学院大学数学科学学院,北京100049 [4]扬州大学数学科学学院,扬州225009

出　　处：《计算数学》2023年第4期497-512,共16页Mathematica Numerica Sinica

基　　金：北京市教育委员会科研计划项目(KM202310853001);北京工业职业技术学院青年教师科研能力提升支持计划项目(BGY2021KY-05QT);国家自然科学基金项目(12171466)资助.

摘　　要：本文对一类变分数阶非线性随机微积分方程初值问题构造了Euler-Maruyama(EM)方法进行数值求解.然后,证明了该EM方法的强稳定性和强收敛性,其强收敛阶为max{1-α^(*),0.5},其中α^(*)=max{α(t)},这里α(t)是Riemann-Liouville变分数阶导数的阶数.最后,用数值试验验证了该EM方法的强收敛阶.This paper constructs a Euler-Maruyama(EM)method for numerically solving a class of variable-order fractional nonlinear stochastic integro-differential equations with initial value.Then,the strong stability and strong convergence of this presented EM method are strictly proved,respectively.The order of strong convergence is max{1-α^(*),0.5},where α^(*)=max{α(t)},hereα(t)is the order of variable-order Riemann-Liouville derivative.Finally,numerical tests are provided to verify the strong convergence of this EM method.

关 键 词：随机微积分方程 变分数阶导数 EULER-MARUYAMA方法 强收敛性 

分 类 号：O241.8[理学—计算数学]