半线性椭圆方程的一个新的双重网格差分算法

A novel two-grid difference algorithm for semilinear elliptic equations

用所提出的双重网格算法研究了半线性椭圆方程,其对粗网格(可以很粗)的非线性解在细网格上进行了几次线性修正.无需求解细网格上的非线性解,且重复算法最后两步,可使解的误差估计达到任意阶精度,并提出了相应的数值算例.

A novel algorithm based on two grid difference method is presented.Three linear corrections on fine grid for the nonlinear solution on coarse grid （it can be extremely coarse） are performed. It＇s unnecessary to get the nonlinear solution on fine grid and any-order accuracy is obtained for error estimate of solution by repeating the last two steps of this algorithm. The numerical resuits validating the theory are also presented.