N阶分歧问题的数值逼近

Numerical Approximation of Corank N Bifurcation Problems

对任意有限阶分歧问题的数值逼近进行了研究。构造了求解一类非退化分歧点及相关参数的扩充系统［１］的逼近形式，采用拟牛顿法来逼近离散后的奇异点及相关参数，该方法中改进的导数矩阵具有分块下三角形式，不仅计算量大大减少，而且具有超线性收敛性。

Numerical approximations of bifurcation problems with arbitrary finite corank are studied. An approximate form of an extended system for approximating a kind of nondegenerate bifurcation points and relevant parameters is constructed. A Newton like iteration method for approximating discrete singular points and relevant parameters is used, and the improved derivative matrix in this method embodies a block lower triangular form, as the result, not only with a lot of computational work being reduced, but also with convergence speed of superlinear being obtained.