Gao, Shunkang; Lin, Jian On the solution of initial value problems of ordinary differential equations by a geometrical method. (Chinese. English summary) Zbl 0637.65076 J. Zhejiang Univ. 21, No. 4, 152-162 (1987). Consider the initial value problem of ordinary differential equations \[ (1)\quad \dot y_ i=f_ i(x,y_ 1,...,y_ n),\quad y_ i(x_ 0)=y_ i\quad 0\quad (i=1,2,...,n). \] Known numerical solutions for (1) include the Euler method, the Runge-Kutta method and others. In this paper, from a geometrical point of view, a numerical solution of (1) is established by applying a Frenet coordinate system in \((n+1)\)-dimensional space. When applying the method, better results are obtained by automatically selecting step sizes. Reviewer: Tian Jinghuang MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems Keywords:geometrical method; step size control; Frenet coordinate system PDFBibTeX XMLCite \textit{S. Gao} and \textit{J. Lin}, J. Zhejiang Univ. 21, No. 4, 152--162 (1987; Zbl 0637.65076)