Accuracy of a numerical method - general definition

• - Define the local truncation error \(\tau\):
• • Error accumulated during one step, assuming perfect knowledge of the true solution
  • \(\tau_k=\|\tilde u(t^k)-u^{k}\|\), assuming \(u^{k-1}=\tilde u (t^{k-1})\)

• - A numerical scheme is said to be accurate of order \(k\), if its local truncation error is in \(\mathcal{O}(h^{k+1})\).

• Explicit Euler is of order \(1\), at every step we add an error in \(\mathcal{O}(h^2)\).