Solved: Consider the initial-value problem y(1) = 5. The
Chapter 9, Problem 18E(choose chapter or problem)
Consider the initial-value problem \(y^{\prime}=2 x-3 y+1\), y(1) = 5. The analytic solution is
\(y(x)=\frac{1}{9}+\frac{2}{3} x+\frac{38}{9} e^{-3(x-1)}\).
(a) Find a formula involving c and h for the local truncation error in the nth step if the RK4 method is used.
(b) Find a bound for the local truncation error in each step if h 0.1 is used to approximate y(1.5).
(c) Approximate y(1.5) using the RK4 method with h = 0.1 and h = 0.05. See Problem 3. You will need to carry more than six decimal places to see the effect of reducing the step size.
Text Transcription:
y^prime=2 x-3 y+1
y(x)=1/9+2/3 x+38/9 e^-3(x-1)
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