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6. Consider the initial value problem dy = -5y + 5t2 + 2t, 0

6. Consider the initial value problem dy = -5y + 5t2 + 2t, 0

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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Numerical/ solve questions number 6
6. Consider the initial value problem dy = -5y + 5t2 + 2t, 0<t<1, y(0) = 1 dt that has exact solution y(t) = t² +e-5t. (a) With h = 0.1, approximate y(0.2) using the Midpoint method h Yi+1 = Yi + hf|t; + 2:Yi +f(ti, y;) i = 0, 1, ... 2 (b) Approximate y(0.3 using the implicit Adams-Moulton three step method h 9 f(t;+1, Yi+1) + 19 f (ti, Yi) – 5 f (t;-1, Yi–1) + f(t;-2, Yi–2) Yi+1 = Yi + 24 and the answers to part (a) with h = 0.1. What is the actual error?
Transcribed Image Text:6. Consider the initial value problem dy = -5y + 5t2 + 2t, 0<t<1, y(0) = 1 dt that has exact solution y(t) = t² +e-5t. (a) With h = 0.1, approximate y(0.2) using the Midpoint method h Yi+1 = Yi + hf|t; + 2:Yi +f(ti, y;) i = 0, 1, ... 2 (b) Approximate y(0.3 using the implicit Adams-Moulton three step method h 9 f(t;+1, Yi+1) + 19 f (ti, Yi) – 5 f (t;-1, Yi–1) + f(t;-2, Yi–2) Yi+1 = Yi + 24 and the answers to part (a) with h = 0.1. What is the actual error?
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