摘要
本文对两点边值问题的广义差分法,当试探函数空间为分片二次多项式空间,检验函数空间为分片线性函数空间时,分析了广义差分解的误差结构。使用格林函数,发现检验函数空间会影响广义差分解在节点处的收敛阶,使它不具备象有限元法那样的超收敛性。进一步我们证明,当广义差分解满足差分条件|δ~4u_i|≤ch^4(其中δ~4u_i 表示半步长的四阶中心差分)时它的误差的渐近展开式可表为 gh^3+O(h^4)的形式,从而使用外推算法可将收敛阶提高到 O(h^4)。
For the generalized difference method of the two-points boundary problem,this paper analyses the structure of the error of the gene- ralized difference solution when the trialfunction space as a piecewise quadratic Lagrange interpolation function space and the test function space as a linear.Using the Greenfunetion,it is discovered that the conver- gent exponet of the generalized difference solutions on the points of division may be affected by the testfunction space,so that it possess not the superconvergence as FEM.Further we prove,when the genera- lized difference solutions satisfy difference condition |δ~4u_j|≤ch^4 (there δ~4u_j:shows 4-classcenter difference),the asymptotic expansion of their errors may be showed by the form gh^3+O(h^4),thus using on extrapola- tion algrithm can improve the convergent exponent to O(h^4).
出处
《贵州大学学报（自然科学版）》
1989年第1期31-42,共12页
Journal of Guizhou University:Natural Sciences
关键词
广义差分法
外推算法
格林函数
generalized difference method
extrapolation algorithm
green function
asymptotic expansion.
