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On the solution of initial value problems of ordinary differential equations by a geometrical method. (Chinese. English summary) Zbl 0637.65076

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
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