摘要
则称二阶完全非线性组(1)是一致抛物的.我们在矩形域Q_T={0≤x≤l,0≤t≤T}(l>0,T>0)上研究方程组(1)
The general difference schemes for the first boundary problem of the comple-tely nonlinear parabolic systems of second order f(x, t, u, u_x, u_(xx), u_t)=0are considered in the rectangular domain Q_T={0≤x≤l, 0≤t≤T}, where u(x,t) and f(x, t, u, p, r, q) are two m-dimensional vector functions with m≥1 for (x, t)∈Q_T and u, p, r, q∈R^m. The existence and the estimates of solutions for the finitedifference system are established by the fixed point technique. The absolute and re-lative stability and convergence of difference schemes are justified by means of a se-ries of a priori estimates. In the present study, the existence of the unique smoothsolution of the original problem is assumed. Similar results for nonlinear and qua-silinear parabolic systems are also obtained.
出处
《计算数学》
CSCD
北大核心
1991年第1期1-5,共5页
Mathematica Numerica Sinica
