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(TRICKY) Approximate y(1.1) for the non-linear initial value problem d?y dy 2y = 0, dx y(0) = 1, y (0) = 1 dx2 1 using the improved Euler's method with h = 0.1. The exact solution is y(x) = so y(1.1) = -10. In this case the approximation is badly 1 - x off. How small a step-size do you need to pick to get the relative error under 10%.

(TRICKY) Approximate y(1.1) for the non-linear initial value problem d?y dy 2y = 0, dx y(0) = 1, y (0) = 1 dx2 1 using the improved Euler's method with h = 0.1. The exact solution is y(x) = so y(1.1) = -10. In this case the approximation is badly 1 - x off. How small a step-size do you need to pick to get the relative error under 10%.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(TRICKY) Approximate y(1.1) for the non-linear initial value problem d?y dy - 2y = 0, y(0) = 1, y(0) = 1 dx2 dx 1 so y(1.1) = -10. In this case the approximation is badly 1- x using the improved Euler's method with h = 0.1. The exact solution is y(x) = off. How small a step-size do you need to pick to get the relative error under 10%.
Transcribed Image Text:(TRICKY) Approximate y(1.1) for the non-linear initial value problem d?y dy - 2y = 0, y(0) = 1, y(0) = 1 dx2 dx 1 so y(1.1) = -10. In this case the approximation is badly 1- x using the improved Euler's method with h = 0.1. The exact solution is y(x) = off. How small a step-size do you need to pick to get the relative error under 10%.
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