数值解多维问题的外推与组合技术的若干新进展

New Developments of Extrapolation Methods and Combination Techniques for Solutions of Multi-dimensional Problems

本文综述近年来数值解多维问题的外推与组合技术的新进展．内容包括分裂外推及其在偏微分方程、多维积分方程、多维数值积分中的应用；Ｃ．Ｚｅｎｇｅｒ的稀疏网格法与组合求解技术；以及解边界积分方程的组合方法．本文通过算例表明这些方法是非常有效的，是解多维问题的钥匙．

This paper states new developments of extrapolation methods and combination techniques for solutions of multi-dimensional problems. It contains splitting extrapolation and its applications to the partial differential equation, the multi-dimensional integral equation and the numerical multiple integration, the sparse grid method and combination method for solving boundary integral equations. The numerical examples given in this paper show that these methods are very efficient for solutions of multi-dimensional problems.