中文摘要：

为求解非线性方程组F（x）=0，提出Newton场线微分方程xs（t）=-（DF（x））^-1F（x），x（0）=x^0．在m重根x^n的中心场域中任取初始点x^0，证明了用前向Euler格式得到的解序列x^n一定收敛到此根，故场线法大范围收敛．由此提出求非线性方程组所有根的场线算法，其有效性为数值试验所证实．

英文摘要：

To find all roots of nonlinear equation system F （x） = 0, Newton field-line differential equation x,（t） = - （DF（x））^-1F（x） ,x（O） =x^0 is proposed. It is proved that taking any initial point x^0 in central field domain of m,ple root x＂, the solution series ｜ x^n｜ computed by forward Euler scheme certainly converges to the root x^n. The field-line method is globally convergent. Then a field-line algorithm for finding all roots of nonlinear equa- tion system is proposed. Its efficiency is shown by numberieal experiments.