西南师范大学学报（自然科学版）
西南師範大學學報（自然科學版）
서남사범대학학보（자연과학판）
JOURNAL OF SOUTHWEST CHINA NORMAL UNIVERSITY
2014年
9期
1-5
,共5页
自由边界问题%有限差分%线性互补%不动点%自适应%预测%校正算法
自由邊界問題%有限差分%線性互補%不動點%自適應%預測%校正算法
자유변계문제%유한차분%선성호보%불동점%자괄응%예측%교정산법
free boundary problem%finite difference%linear complementarity%fixed point%self-adaptive%prediction-correct algorithm
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。
對一類自由邊界問題，提齣瞭基于線性互補問題的自適應預測-校正算法。用有限差分對微分模型離散化後得到一箇正定線性互補問題，該問題等價于一箇不動點問題，從而得到求解線性互補問題的自適應預測-校正算法。用正定性及投影基本性質可證明算法收斂性。給齣瞭具體的算法過程，數值結果錶明瞭算法的可行性和有效性。
대일류자유변계문제，제출료기우선성호보문제적자괄응예측-교정산법。용유한차분대미분모형리산화후득도일개정정선성호보문제，해문제등개우일개불동점문제，종이득도구해선성호보문제적자괄응예측-교정산법。용정정성급투영기본성질가증명산법수렴성。급출료구체적산법과정，수치결과표명료산법적가행성화유효성。
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 .
