NUMERICAL-ANALYSIS Course

Backward

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It's quite the same as the forward Euler method, with a little difference:

\[ \left\lbrace \begin{array}{l} z_0 = y_0 \\ z_{k+1} = z_k + (t_{k+1} - t_k) \times f(t_{k+1}, z_{k+1})\quad \forall k < N \end{array} \right . \]

It is called backward because the expression of $z_{k+1}$ depends on itself; the unknown value depends on itself, which made the calculations less easy.