黑龙江大学自然科学学报
黑龍江大學自然科學學報
흑룡강대학자연과학학보
JOURNAL OF NATURAL SCIENCE OF HEILONGJIANG UNIVERSITY
2009年
6期
711-717
,共7页
逼近解%非线性伪抛物方程%再生核空间%非局部边值条件
逼近解%非線性偽拋物方程%再生覈空間%非跼部邊值條件
핍근해%비선성위포물방정%재생핵공간%비국부변치조건
approximate solution%nonlinear pseudoparabolic equation%reproducing kernel space%nonlocal boundary condition
探讨在再生核空间用迭代法求解一维非线性伪抛物方程.证明逼近解u_n(x,t)收敛于真解u(x,t),且u_n(x,t)的各阶偏导数亦收敛于u(x,t)相应阶的偏导数.在一个完全标准正交系下,u_n(x,t)是最佳逼近解.
探討在再生覈空間用迭代法求解一維非線性偽拋物方程.證明逼近解u_n(x,t)收斂于真解u(x,t),且u_n(x,t)的各階偏導數亦收斂于u(x,t)相應階的偏導數.在一箇完全標準正交繫下,u_n(x,t)是最佳逼近解.
탐토재재생핵공간용질대법구해일유비선성위포물방정.증명핍근해u_n(x,t)수렴우진해u(x,t),차u_n(x,t)적각계편도수역수렴우u(x,t)상응계적편도수.재일개완전표준정교계하,u_n(x,t)시최가핍근해.
An iterative method is given to solve one-dimensional nonlinear pseudoparabolic equation in the reproducing space. It is proved that the approximate sequence u_n(x, t) converges to the exact solution u(x,t). Moreover, the partial derivatives of u_n(x,t) are also convergent to the partial derivatives of u(x, t). And the approximate sequence u_n(x, t) is the best approximation under a complete normal orthogonal system.
