代写M426 H28帮做R编程

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.