Use the fourth-order Runge-Kutta subroutine with h = 0.25 to approximate the solution to the initial value problem below, at x = 1. Using the Taylor method of order 4, the solution to the initial value problem, at x = 1, is (1) = 3.369395. Compare your approximation with the one obtained using the Taylor af method. Note whether or not is bounded. y'=x+3-y, y(0) = 3 Əf Let y'=f(x,y). Find and determine whether or not it is bounded on the vertical strip S= {(x,y): 0
Use the fourth-order Runge-Kutta subroutine with h = 0.25 to approximate the solution to the initial value problem below, at x = 1. Using the Taylor method of order 4, the solution to the initial value problem, at x = 1, is (1) = 3.369395. Compare your approximation with the one obtained using the Taylor af method. Note whether or not is bounded. y'=x+3-y, y(0) = 3 Əf Let y'=f(x,y). Find and determine whether or not it is bounded on the vertical strip S= {(x,y): 0
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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Transcribed Image Text:Use the fourth-order Runge-Kutta subroutine with h = 0.25 to approximate the solution to the initial value problem below, at x = 1. Using the Taylor method
of order 4, the solution to the initial value problem, at x = 1, is (1) = 3.369395. Compare your approximation with the one obtained using the Taylor
af
method. Note whether or not is bounded.
y'=x+3-y, y(0) = 3
Əf
Let y'=f(x,y). Find and determine whether or not it is bounded on the vertical strip S= {(x,y): 0<x<1, -∞<y<∞). Select the correct choice below
dy
and fill in the answer box to complete your choice.
Əf
O A. y(x,y)= is bounded.
af
O B. a (x,y)=
is not bounded.
Use the fourth-order Runge-Kutta subroutine with h = 0.25 to approximate the solution to the initial value problem at x = 1.
K(1) =
(Round to six decimal places as needed.)
Let p(x) denote the actual solution. Which approximation is better? Select the correct choice below and fill in the answer box to complete your choice.
(Round to six decimal places as needed.)
O A. The Taylor approximation is better, because the error is $T(1)-(1)| = .
OB. The Runge-Kutta approximation is better, because the error is |K(1)-(1)| = .
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