Mean square solution of Bessel differential equation with uncertainties

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• 作者：J.-C. Corté ; s^a ; ^{jccortes@imm.upv.es" class="auth_mail" title="E-mail the corresponding author} ; L. Jó ; dar^a ; ^{ljodar@imm.upv.es" class="auth_mail" title="E-mail the corresponding author} ; L. Villafuerte^b ; ^{laura.villafuerte@unach.mx" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Random differential equation ; LpLp-random calculus ; Bessel differential equation
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：309
• 期：Complete
• 页码：383-395
• 全文大小：495 K

文摘

This paper deals with the study of a Bessel-type differential equation where input parameters (coefficient and initial conditions) are assumed to be random variables. Using the so-called class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716300139&_mathId=si58.gif&_user=111111111&_pii=S0377042716300139&_rdoc=1&_issn=03770427&md5=50ce35c34b772812b61eabfdb6966a5f" title="Click to view the MathML source">L_pclass="mathContainer hidden">class="mathCode">$L_p$-random calculus and assuming moment conditions on the random variables in the equation, a mean square convergent generalized power series solution is constructed. As a result of this convergence, the sequences of the mean and standard deviation obtained from the truncated power series solution are convergent as well. The results obtained in the random framework extend their deterministic counterpart. The theory is illustrated in two examples in which several distributions on the random inputs are assumed. Finally, we show through examples that the proposed method is computationally faster than Monte Carlo method.