用初值问题方法求解边值问题的同伦延拓技术

Homotopy continuation technology for solving boundary value problems using solution methods for initial value problems

讨论了用初值问题方法求解非线性微分方程边值问题的同伦延拓技术。重点介绍了同伦延拓PC(Predic tor Corrector)技术及其在边值问题求解中的应用 ,并给出了几项求解策略 ,包括矩阵QR分解、矩阵广义逆、Broyden秩 1校正等。结合PC方法 ,采用数值软件Matlab进行编程 ,数值结果表明该方法是非常有效的。

Some methods for solving the initial value problems can be used to solve the boundary value problems of nonlinear differential equation. The numerical continuation technologies were discussed. Especially, the emphasis was laid on predictor-corrector (PC) technology and its application to solve the boundary value problems. Several strategies including QR decomposition, generalized inverse of matrix, Broyden rank-1 correction were given. Some programs of Matlab were computed with PC technology. The numerical continuation results proved the effectiveness of the methodology.