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Question
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1. Let f(t, x) (0,1] × [x − b, xo +b] be a bivariate function with bounded partial
derivatives up to order 3. Consider the following initial value problem,
dax
f(t, x) for tЄ (0,1],
r(0)) = To.
==
dt
(1)
For N = N, we divide the interval [0,1] by the N + 1 mesh points,
=
0 to, t₁h,,tN = Nh = 1,
with h=1/N as the step size.
(a) Write down the 6-method with 0 = 0.5 for (④). Is it an explicit method?
(b) Repeat the global error estimate for the explicit Euler method to derive the
global error estimate for the 0-method with 0 = 0.5.