Problem. For the initial value problem dy/dx = x2 + y?, y(0) = 0, show that the third Picard approximation is Уз (х) — 63 11 2079 59535 Compute y3(1). The fourth-order Runge-Kutta method yields y(1) s 0.350232, both with step size h = 0.05 and with step size h = 0.025.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 47CR
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Problem.
For the initial value problem dy/dx = x2 + y?, y(0) = 0,
show that the third Picard approximation is
Уз (х) —
63
11
2079
59535
Compute y3(1). The fourth-order Runge-Kutta method
yields y(1) s 0.350232, both with step size h = 0.05 and
with step size h = 0.025.
Transcribed Image Text:Problem. For the initial value problem dy/dx = x2 + y?, y(0) = 0, show that the third Picard approximation is Уз (х) — 63 11 2079 59535 Compute y3(1). The fourth-order Runge-Kutta method yields y(1) s 0.350232, both with step size h = 0.05 and with step size h = 0.025.
Expert Solution
Step 1

Given:

dydx=x2+y2 and y(0)=0

To Show:

The third Picard approximation is: y3x=13x3+163x7+22079x11+159535x15 and find y31.

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