# Numerical Experiments

For the equation y'=x with y(0)=1, here are some explicit suggestions to look at how the dependence of the error at t=1 depends on choices of method, stepsize, and rounding technique.

Euler Method 64 Bit:
Try step sizes of , , and . Can you see a truncation error approximately proportional to ?
Midpoint Euler Method 64 Bit:
Try step sizes of and . Can you see a truncation error approximately proportional to ?
Midpoint Euler Method 16 Bit Trunc round:
Try step sizes of , , and . Can you see a roundoff error approximately proportional to ?
Midpoint Euler Method 16 Bit Trunc down:
Try step sizes of , , and . Can you see a roundoff error approximately proportional to ?

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2002-08-23