Truncation error (numerical integration)

Truncation errors in numerical integration are of two kinds: local truncation errors – the error caused by one iteration, and global truncation errors – the cumulative error caused by many iterations. == Definitions == Suppose we have a continuous differential equation y ′ = f ( t , y ) , y ( t 0 ) = y 0 , t ≥ t 0 {\displaystyle y'=f(t,y),\qquad y(t_{0})=y_{0},\qquad t\geq t_{0}} and we wish to compute an approximation y n {\displaystyle y_{n}} of the true solution y ( t n ) {\displaystyle y(t_{n})} at discrete time steps t 1 , t 2 , … , t N {\displaystyle t_{1},t_{2},\ldots ,t_{N}} .

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