M426 H28
1. Two steps of Euler h = 0.1.
y′ = −2ty; y(0) = 2; 0 ≤ t ≤ 0.2.
Given solution y = 2e
−t2. Find one step error and the global error. Show that they are bounded by the theory.
2. Two steps of Euler h = 0.2.
y′ = y + t; y(0) = 2; 0 ≤ t ≤ 0.4.
Given the solution y = −1 − t + 3et. Find one step error and the global error. Show that they are bounded by the theory.
3. Find y(T) by the adaptive Euler method with h = 0.2 and T L = 0.1.
y′ = ty; y(1) = −2; 1 ≤ t ≤ 1.2.
Check the final error.
4. Find y(T) by the adaptive Euler method with ini-tial h0 = 0.2 and T L = 0.1.
y′ = 1 + 2y; y(0) = 1; 0 ≤ t ≤ 0.2.
Check the final error.