Consider the initial value problem: Solution: y' = (y -0.01x²)² sin(x²) + 0.02x; y(0) = 0.4 y = 1/[2.5 - S(x)] +0.01x² where S(x) is the Fresnel integral a. Solve the above ODE by Euler, midpoint, and RK4 methods for 0 ≤ x ≤ 5 with step h = 0.2
Consider the initial value problem: Solution: y' = (y -0.01x²)² sin(x²) + 0.02x; y(0) = 0.4 y = 1/[2.5 - S(x)] +0.01x² where S(x) is the Fresnel integral a. Solve the above ODE by Euler, midpoint, and RK4 methods for 0 ≤ x ≤ 5 with step h = 0.2
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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![Consider the initial value problem:
Solution:
y' = (y -0.01x²)² sin(x²) + 0.02x;
y(0) = 0.4
y = 1/[2.5 - S(x)] + 0.01x² where S(x) is the Fresnel integral
a. Solve the above ODE by Euler, midpoint, and RK4 methods for 0≤x≤5 with step h = 0.2
b. Compare the errors for x = 1, 3, 5 and comment.
c. Graph solution curves of the ODE above for various positive and negative initial values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2337193-468b-4359-91e5-941c8ab4eff6%2Fcdb108ab-a38f-4a12-9762-38763acbcc1a%2Fe3rub9_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem:
Solution:
y' = (y -0.01x²)² sin(x²) + 0.02x;
y(0) = 0.4
y = 1/[2.5 - S(x)] + 0.01x² where S(x) is the Fresnel integral
a. Solve the above ODE by Euler, midpoint, and RK4 methods for 0≤x≤5 with step h = 0.2
b. Compare the errors for x = 1, 3, 5 and comment.
c. Graph solution curves of the ODE above for various positive and negative initial values.
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