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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.

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