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.
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)
出处
《计算数学》
CSCD
北大核心
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.
