Given the initial value problem dy =0, x + y + sin (x + y) + cos (xy) + = 0, y (0) = 0, dr approximate y (1), with h = 0.1.
Given the initial value problem dy =0, x + y + sin (x + y) + cos (xy) + = 0, y (0) = 0, dr approximate y (1), with h = 0.1.
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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![Question 5
(a) Given the initial value problem
dy
x + y + sin (x + y) + cos (xy) +
= 0, y (0) = 0,
dx
approximate y (1), with h = 0.1.
(b) The Runge-Kutta method of order 2 (RK2) with h = 0.1 is used to solve
dy
-y + xy
dx
with y(0) = 1 in order to find y(0.3) correct to four decimal places. Assuming
that the local error in RK2 is given by
h3
-" (ξ), ξε [, 141],
Ei+1
6
estimate an upper bound for the global error at x =
:0.3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac4a4fe9-6ca1-4a14-bf1e-fb9fc430b0b5%2F94421982-cfc7-45e6-938d-732742372247%2Fcg2pysf_processed.png&w=3840&q=75)
Transcribed Image Text:Question 5
(a) Given the initial value problem
dy
x + y + sin (x + y) + cos (xy) +
= 0, y (0) = 0,
dx
approximate y (1), with h = 0.1.
(b) The Runge-Kutta method of order 2 (RK2) with h = 0.1 is used to solve
dy
-y + xy
dx
with y(0) = 1 in order to find y(0.3) correct to four decimal places. Assuming
that the local error in RK2 is given by
h3
-" (ξ), ξε [, 141],
Ei+1
6
estimate an upper bound for the global error at x =
:0.3.
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