Note on Mass-Spring numerical solution

• - Non-linear ODE

• - Large \(K_{ij}\) : good length preservation, but stiff ODE
• • \(\Rightarrow\) divergence of explicit schemes.
• - Avoid explicit Euler (divergence)

• - Semi-implicit Euler/Verlet works fine for low \(K_{ij}\)
• • Semi-implicit Euler + PBD allows simple integration + stable stiff springs
  • [Muller et al. PBD , Inextensible clothing in Computer Games ]

• - RK4 more accurate (but higher complexity than Verlet)

• - Implicit Euler : requires linearization, but very stable