Truncation error (numerical integration)

Truncation errors in numerical integration are of two kinds:

Suppose we have a continuous differential equation

and we wish to compute an approximation ${\displaystyle y_{n}}$ of the true solution ${\displaystyle y(t_{n})}$ at discrete time steps ${\displaystyle t_{1},t_{2},\ldots ,t_{N}}$. For simplicity, assume the time steps are equally spaced:

Suppose we compute the sequence ${\displaystyle y_{n}}$ with a one-step method of the form

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