Solve the above ODE by RK4 method 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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ADVANCED MATH! (You may use MS EXCEL for the GRAPHS)
a. Solve the above ODE by RK4 method for 0 ≤ x ≤ 5 with step h= 0.2
b. Compute the errors for x = 1, 3, 5. Expalin the findings in sentences.
c. Graph solution curves of the ODE above for various positive (x = 0.1, 0.2, 0.4, 0.6, ...) and negative (x = ..., -1.0, -0.8, -0.6, -0.4, -0.2) initial values.
![Consider the initial value problem:
y' = (y -0.01x²)² sin(x²) + 0.02x; y(0) = 0.4
Solution:
where S(x) is the Fresnel integral
14
y = 1/[2.5 - S(x)] +0.01x²
0.5
C(x)
per profe
1
S(x) = f sin t² dt
2
Fig. $55. Fresnel integrals
LE](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf06c3b2-5589-416a-92cb-31f24a9dfab6%2F9a5c7ab1-d4e2-430a-8194-7b923660398f%2Fg2lkib9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem:
y' = (y -0.01x²)² sin(x²) + 0.02x; y(0) = 0.4
Solution:
where S(x) is the Fresnel integral
14
y = 1/[2.5 - S(x)] +0.01x²
0.5
C(x)
per profe
1
S(x) = f sin t² dt
2
Fig. $55. Fresnel integrals
LE
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