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Geometrically Derived Difference Formulae for the Numerical Integration of Trajectory Problems

机译：轨迹问题数值积分的几何推导差分公式

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摘要

The term 'trajectory problem' is taken to include problems that can arise, for instance, in connection with contour plotting, or in the application of continuation methods, or during phase-plane analysis. Geometrical techniques are used to construct difference methods for these problems to produce in turn explicit and implicit circularly exact formulae. Based on these formulae, a predictor-corrector method is derived which, when compared with a closely related standard method, shows improved performance. It is found that this latter method produces spurious limit cycles, and this behavior is partly analyzed. Finally, a simple variable-step algorithm is constructed and tested.

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Mcleod, R. J. Y.; Sanz-serna, J. M.;
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年度 1981
页码 p.1-34
总页数 34
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Analytic geometry; Boundary value problems; Differences; Differential equations; Numerical integration; Problem solving; Trajectories; Algorithms; Curves (Geometry); Jacobi matrix method; Nonlinear equations; Series expansion; Taylor series; Truncation errors;

机译：解析几何;边值问题;差分;微分方程;数值积分;问题解决;轨迹;算法;曲线（几何）;雅可比矩阵法;非线性方程;级数展开;泰勒级数;截断误差;

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7. Geometrically derived difference formulae for the numerical integration of trajectory problems [O] . Mcleod R. J. Y., Sanz-Serna J. M. 1981

机译：轨迹问题数值积分的几何导出差分公式

Geometrically Derived Difference Formulae for the Numerical Integration of Trajectory Problems

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