Beyond the hypothesis of boundedness for the random coefficient of the Legendre differential equation with uncertainties
作者：
Highlights：
• We study the Legendre random differential equation with unbounded input coefficient.
• The Fröbenius method allows for constructing the mean square solution.
• We assume at most linear growth of the Lebesgue norm of the equation coefficient.
• The assumption is closely related to the finiteness of the moment-generating function.
• The numerical examples illustrate the approximation of moments.
摘要
•We study the Legendre random differential equation with unbounded input coefficient.•The Fröbenius method allows for constructing the mean square solution.•We assume at most linear growth of the Lebesgue norm of the equation coefficient.•The assumption is closely related to the finiteness of the moment-generating function.•The numerical examples illustrate the approximation of moments.
论文关键词：Random differential equation,Fröbenius method,Mean square calculus,Mean fourth calculus,Moment-generating function
论文评审过程：Received 28 November 2019, Revised 27 April 2020, Accepted 22 August 2020, Available online 11 September 2020, Version of Record 11 September 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125638
