0
votes
0answers
21 views

Solving coupled nonlinear ODEs, controlling numerical instability through numerical viscosity

I'm solving a problem numerically that takes the form $ Q_{ij} \ddot{y}_j +S_{ijk}\dot{y}_j\dot{y}_k +V_i=0$, where $(Q_{ij},S_{ijk},V_i) $ are all low order polynomial functions of the dependent ...
11
votes
5answers
1k views

Basic mechanics problems, unsolvable by brute-force numerical integration

I'm looking for simple problems in theoretical mechanics that are impossible or unreasonably difficult to solve by means of "brute-force" numerical integration of Newton or Euler-lagrange equations. ...