中文

Integrating Factors and ODE Patterns

计算物理 2025-06-10 v2 数学物理 微分几何 math.MP

摘要

A systematic algorithm for building integrating factors of the form mu(x,y') or mu(y,y') for non-linear second order ODEs is presented. When such an integrating factor exists, the algorithm determines it without solving any differential equations. Examples of ODEs not having point symmetries are shown to be solvable using this algorithm. The scheme was implemented in Maple, in the framework of the ODEtools package and its ODE-solver. A comparison between this implementation and other computer algebra ODE-solvers in tackling non-linear examples from Kamke's book is shown.

关键词

引用

@article{arxiv.physics/9711027,
  title  = {Integrating Factors and ODE Patterns},
  author = {E. S. Cheb-Terrab and A. D. Roche},
  journal= {arXiv preprint arXiv:physics/9711027},
  year   = {2025}
}

备注

23 pages, LaTeX, revised version for the Journal of Symbolic Computation. Soft-package (On-Line help) and sample MapleV sessions available at: http://dft.if.uerj.br/odetools.htm or http://lie.uwaterloo.ca/odetools.htm HTML Demo at: http://lie.uwaterloo.ca/demos/odetools_intfactor.html