自由边界问题的自适应预测-校正算法

对一类自由边界问题,提出了基于线性互补问题的自适应预测-校正算法.用有限差分对微分模型离散化后得到一个正定线性互补问题,该问题等价于一个不动点问题,从而得到求解线性互补问题的自适应预测-校正算法.用正定性及投影基本性质可证明算法收敛性.给出了具体的算法过程,数值结果表明了算法的可行性和有效性.

On a Self-Adaptive Prediction-Correct Algorithm for Free Boundary Problem

A self-adaptive prediction-correct algorithm based on linear complementarity problem for solving the free boundary problem has been studied in this paper .The problem is discretized in finite difference method and formulated as a positive definite linear complementarity problem ,w hich is equivalent to a fixed point problem .Then a self-adaptive prediction-correct algorithm has been proposed .With positive defi-niteness and projection principle ,the convergence of the algorithm has been proved .The detailed process of the algorithm has been provided ,and the numerical results presented illustrate the feasibility and effec-tiveness of this algorithm .