Choose a problem and the number of steps N. See what halving h does to the error, and use the error bound of Theorem 5.9 to choose N for a target error, as on slide 12.
Exact value y(b)—
Euler's method wN—
Absolute error |y(b) − wN|—
Error bound at t = b (Theorem 5.9)—
Exact solution and Euler's method
Halving h
Choose N for a target error
|y(b) − wN| ≤
Type 0.01, 1e-3 or 10^-4.
Enter a positive number for the target error, for example 0.01 or 1e-3.
Make the error bound of Theorem 5.9 at t = b at most the target and solve for N. The lab also finds the smallest N the actual error needs.