Consider the initial-value problem y=9y, y(0) - 1. The analytic solution is y(x) = e. (a) Approximate y(0.1) using one step and the fourth-order RK4 method. (Round your answer to six decimal places.) (b) Find a bound for the local truncation error in y1- (Proceed as in this example. Round your answer to nine decimal places.) (c) Compare the actual error in y with your error bound. The actual error, rounded to nine decimal places, is प Select v the local truncation error found in part (b).
Consider the initial-value problem y=9y, y(0) - 1. The analytic solution is y(x) = e. (a) Approximate y(0.1) using one step and the fourth-order RK4 method. (Round your answer to six decimal places.) (b) Find a bound for the local truncation error in y1- (Proceed as in this example. Round your answer to nine decimal places.) (c) Compare the actual error in y with your error bound. The actual error, rounded to nine decimal places, is प Select v the local truncation error found in part (b).
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:Consider the initial-value problem y'= 9y, y(0) = 1. The analytic solution is y(x) - e9K.
(a) Approximate y(0.1) using one step and the fourth-order RK4 method. (Round your answer to six decimal places.)
(b) Find a bound for the local truncation error in y1. (Proceed as in this example. Round your answer to nine decimal places.)
(c) Compare the actual error in yi with your error bound.
The actual error, rounded to nine decimal places, is
which is -Select v the local truncation error found in part (b).
(d) Approximate y(0.1) using two steps and the RK4 method. (Round your answer to six decimal places.)
(e) Verify that the global truncation error for the RK4 method is O(h") by comparing the errors in parts (a) and (d).
With global truncation error O(h*), when the step size
The actual error for the answer in (d), rounded to nine decimal places, is
h = 0.05 to be approximately -Select-
halved we expect the error for
v the error when h = 0.1. Comparing the two errors we see that this -Solect-v the case.
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