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6. Let f(t) be some smooth function: f. f(t) are continuous and bounded. Use the Euler method with step size k to solve the following ODE v=f(t), y(0) - 0. The above solution has an exact solution y(t) = f(s)ds. Compare the solutions y ob- tained by the Euler method and improved Euler method with y(t). For fixed t ≤ 1, show that yn-y(nk) = n − y(t) → 0 as k→ 0 and n = You do not need to prove the convergence rate O(k). Hint: Use integral.

6. Let f(t) be some smooth function: f. f(t) are continuous and bounded. Use the Euler method with step size k to solve the following ODE v=f(t), y(0) - 0. The above solution has an exact solution y(t) = f(s)ds. Compare the solutions y ob- tained by the Euler method and improved Euler method with y(t). For fixed t ≤ 1, show that yn-y(nk) = n − y(t) → 0 as k→ 0 and n = You do not need to prove the convergence rate O(k). Hint: Use integral.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Let f(t) be some smooth function: f. f(t) are continuous and bounded. Use the Euler method with step size k to solve the following ODE =f(t). 9(0)=0. The above solution has an exact solution y(t) = f(s)ds. Compare the solutions Job- tained by the Euler method and improved Euler method with y(t). For fixed t ≤ 1, show that yn-y(nk) = n − y(t) → 0 as k→ 0 and n =. You do not need to prove the convergence rate O(k). Hint: Use integral.
Transcribed Image Text:6. Let f(t) be some smooth function: f. f(t) are continuous and bounded. Use the Euler method with step size k to solve the following ODE =f(t). 9(0)=0. The above solution has an exact solution y(t) = f(s)ds. Compare the solutions Job- tained by the Euler method and improved Euler method with y(t). For fixed t ≤ 1, show that yn-y(nk) = n − y(t) → 0 as k→ 0 and n =. You do not need to prove the convergence rate O(k). Hint: Use integral.
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