摘要
Gronwall不等式在对偏微分方程近似解的估计中应用十分广泛,对差分方程做先验估计和误差估计时常常会遇到变系数的差分方程的情形。首先把离散的常系数Gronwall不等式推广到离散的变系数差商不等式,其次给出了离散的常系数Gronwall不等式的证明方法——归纳假设方法,并且利用归纳假设方法对离散的变系数差商不等式进行了证明,通过对差商不等式的适当放缩,最后得到了变系数差商不等式的无穷大模估计式。
Gronwall inequality is widely used in the estimation of approximate solution of partial differential equations.We often have variant coefficient in prior estimation and error estimation of the difference equations.First,the paper extended the discrete constant coefficient Gronwall inequality to the variant coefficient situation.Second,the proof method of constant coefficient Gronwall inequality—induction hypothesis method is given and induction hypothesis method is used to proof the variant coefficient difference inequality.At last,the infinite module of variant coefficient quotient inequality is obtained.
出处
《沈阳师范大学学报（自然科学版）》
CAS
2010年第4期477-479,共3页
Journal of Shenyang Normal University:Natural Science Edition
基金
黑龙江省教育厅科学研究项目(11544048)
关键词
无穷大模
差商
先验估计
infinite module
difference quotient
prior estimation
