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Repeat Problem 17 for the initial-value problem y′ = e–y, y(0) = 0. The analytic solution is y(x) = ln(x + 1). Approximate y(0.5). See Problem 5 in Exercises 2.6.
17. Consider the initial-value problem y′ = 2x – 3y + 1, y(1) = 5. The analytic solution is
- (a) Find a formula involving c and h for the local truncation error in the nth step if Euler’s 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 h = 0.1 and h = 0.05 with Euler’s method. See Problem 1 in Exercises 2.6.
- (d) Calculate the errors in part (c) and verify that the global truncation error of Euler’s method is O(h).
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Chapter 9 Solutions
Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's A ... Applications, 11th Edition, Single-Term
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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