Numerical treatment of stochastic delay differential equations: A global error bound
Numerical treatment of stochastic delay differential equations: A global error bound
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DOI：
10.1016/j.cam.2019.04.011
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
Bahar Akhtari-
中科院分区：
文献类型：
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作者：
Bahar Akhtari-
在随机时滞微分方程数值解的误差分析的推动下，提出了一个新结果，表明该格式的收敛速度依赖于两个单独的量p和q，其中前者是基础格式的全局阶数，后者是逼近系统历史的插值阶数。作为一个客观实例，利用强收敛意义上的全局阶数 0.5、1 和 1.5 的随机龙格库塔 (SRK) 格式来制定三个一步格式来近似解决问题。此外，这些方案的均方稳定性将渐近发展。最后，通过一些测试问题来验证理论结果。
Motivated by the error analysis of numerical solution for stochastic delay differential equations, a new result indicating the dependency of convergence rate of the scheme on two separate quantities p and q, where the former is the global order of underlying scheme and the latter is that of interpolation approximating the history of system, is presented. As an objective instance, the stochastic Runge–Kutta (SRK) schemes of global order 0.5, 1 and 1.5, in the strong convergence sense are utilized to formulate three one-step schemes to approximate the solution of the problem. Moreover, the mean-square stability of these schemes will be asymptotically developed. Finally, the theoretical results will be confirmed by some test problems.