| 线性抛物型积分微分方程的扩展混合体积元方法 |
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| 引用本文： | 朱爱玲,姜子文,徐强.线性抛物型积分微分方程的扩展混合体积元方法[J].高等学校计算数学学报,2009,31(3). |
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| 作者姓名： | 朱爱玲 姜子文 徐强 |
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| 作者单位： | 山东师范大学数学科学学院,济南,250014 |
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| 基金项目： | 国家自然科学基金，山东省自然科学基金 |
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| 摘 要： | 1 引言 考虑线性抛物型积分微分方程初边值问题: {pt(x,t)-▽.{A(x,t)▽p(x,t) +∫t0 B(x,t,τ)▽p(x,τ)dτ}=f(x,t),(x,t)∈Ω×(0,T],(1.1) p(x,0):p0(x), x∈Ω, p(x,t)=0, (x,t)∈(a)Ω×(0,T]. 这里x=(x,y),Ω=(a,b)×(c,d),(e)Ω是区域Ω的边界,p为未知函数,A=(aij)2×2为已知的对称正定矩阵,B=(bij)2×2为已知矩阵,而且aij,bij,(aij)t(i,j=1,2)光滑有界,f∈L2(Ω).
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| 关 键 词： | 引理 混合体积 三角不等式 高等学校 扩展 抛物型积分微分方程 元方法 线性 |
EXPANDED MIXED COVOLUME METHOD FOR THE LINEAR INTEGRO-DIFFERENTIAL EQUATION OF PARABOLIC TYPE |
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| Zhu Ailing,Jiang Ziwen,Xu Qiang.EXPANDED MIXED COVOLUME METHOD FOR THE LINEAR INTEGRO-DIFFERENTIAL EQUATION OF PARABOLIC TYPE[J].Numerical Mathematics A Journal of Chinese Universities,2009,31(3). |
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| Authors: | Zhu Ailing Jiang Ziwen Xu Qiang |
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| Institution: | Zhu Ailing Jiang Ziwen Xu Qiang (School of Mathematical Sciences,Shandong Normal University,Jinan 250014) |
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| Abstract: | In this paper,an expanded mixed covolume scheme for the linear integro-differential equation of parabolic type is proposed.The error analysis of the expanded mixed covolume scheme is presented and the optimal order error estimate in L~2 is obtained with the lowest order Raviart-Thomas mixed element space.Finally,a numerical example is given. |
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| Keywords: | linear integro-differential equation of parabolic type expanded mixed covolume method error estimate |
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