Answered: Consider the initial-value problem y' =…

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

Consider the initial-value problem y' = 7y, y(0) = 1. The analytic solution is y(x) = e7x. (a) Approximate y(0.1) using one step and the fourth-order RK4 method. (Round your answer to six decimal places.) 2.0122 Incorrect: Your answer is incorrect. (b) Find a bound for the local truncation error in y1. (Round your answer to nine decimal places.) 0.493369413 Incorrect: Your answer is incorrect. (c) Compare the error in y1 with your error bound. The actual error, rounded to nine decimal places, is 0.0015818745 Correct: Your answer is correct. , which is less than Correct: Your answer is correct. 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.) 2.013753 Incorrect: Your answer is incorrect. (e) Verify that the global truncation error for the RK4 method is O(h4) by comparing the errors in parts (a) and (d). The actual error for the answer in (d), rounded to nine decimal places, is Incorrect: Your answer is incorrect. . With global truncation error O(h4), when the step size is halved we expect the error for h = 0.05 to be approximately one-sixteenth Correct: Your answer is correct. the error when h = 0.1. Comparing the two errors we see that this is Correct: Your answer is correct. the case.

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