本文關(guān)鍵詞： 隨機(jī)非自伴波方程 有限元方法 非自伴算子 cosine算子函數(shù) 強(qiáng)收斂　出處：《計(jì)算數(shù)學(xué)》2017年01期 　論文類型：期刊論文

【摘要】：本文研究了由白噪音驅(qū)動(dòng)的隨機(jī)非自伴波方程的有限元近似,由于線性算子A非自伴,不能應(yīng)用A的特征值和特征向量,從而得到的結(jié)果更具有一般性.空間離散上采用標(biāo)準(zhǔn)的有限元法,并借助強(qiáng)連續(xù)算子函數(shù)的性質(zhì),得到了該方程的強(qiáng)收斂誤差估計(jì).本文方法也適用于多維情況的分析.最后用數(shù)值算例驗(yàn)證了理論分析的正確性.
[Abstract]:In this paper, the finite element approximation of stochastic nonadjoint wave equation driven by white noise is studied. Because the linear operator A is not self-adjoint, the eigenvalue and eigenvector of A can not be applied. The results obtained are more general. The standard finite element method is used in space discretization and the properties of strong continuous operator functions are used. The strong convergence error estimate of the equation is obtained. The method in this paper is also applicable to the analysis of multidimensional cases. Finally, the correctness of the theoretical analysis is verified by a numerical example.
【作者單位】： 北京航空航天大學(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院;北京科技大學(xué)數(shù)理學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(61271010) 北京市自然科學(xué)基金(4152029)資助項(xiàng)目
【分類號(hào)】：O241.82
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本文編號(hào)：1493721