Explicit Euler - study case

1D spring

• - True solution: permanent oscillation

• - Numerical scheme: \(\left(\begin{array}{c}p \\ v\end{array}\right)^{k+1} = \left(\begin{array}{cc}1 & h \\ -K/m\,h & 1 \end{array}\right)\left(\begin{array}{c} p \\ v\end{array}\right)^k+\left(\begin{array}{c}0 \\ K/m\,h\;l^0\end{array}\right)\)

• red: true solution
• red: numerical solution