Consider the following initial value problem: v(t) = e*()-°, y(4) = b. It is known that the exact solution is y(t) = 9 – In(4 + e* – t). (9.1) Euler's method is used to find the approximation of the solution for the initial value problem on the interval [4, 7] with 6 time intervals. It is known that y = 3.00248. Find an approximation for y(7) rounded to 5 decimal places. Also round your answer in each step to 5 decimal places. Use the rounded value in the next step. (9.2) Calculate the local error e4. Do not round answers for any intermediate steps. Give your final answer rounded to 4 significant digits. (9.3) Calculate the global error E. Do not round answers for any intermediate steps. Give your final answer rounded to 4 significant digits.
Consider the following initial value problem: v(t) = e*()-°, y(4) = b. It is known that the exact solution is y(t) = 9 – In(4 + e* – t). (9.1) Euler's method is used to find the approximation of the solution for the initial value problem on the interval [4, 7] with 6 time intervals. It is known that y = 3.00248. Find an approximation for y(7) rounded to 5 decimal places. Also round your answer in each step to 5 decimal places. Use the rounded value in the next step. (9.2) Calculate the local error e4. Do not round answers for any intermediate steps. Give your final answer rounded to 4 significant digits. (9.3) Calculate the global error E. Do not round answers for any intermediate steps. Give your final answer rounded to 4 significant digits.
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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![Consider the following initial value problem:
y (t) = ev()-9
y(4) = b.
It is known that the exact solution is y(t) = 9 – In(4 + e" – t).
(9.1) Euler's method is used to find the approximation of the solution for the initial value
problem on the interval [4, 7] with 6 time intervals. It is known that y2 = 3.00248. Find
an approximation for y(7) rounded to 5 decimal places. Also round your answer in each
step to 5 decimal places. Use the rounded value in the next step.
(9.2) Calculate the local error e4. Do not round answers for any intermediate steps. Give
your final answer rounded to 4 significant digits.
(9.3) Calculate the global error E4. Do not round answers for any intermediate steps.
Give your final answer rounded to 4 significant digits.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23c82962-fdd3-4aae-a199-ce5241f64aad%2Fa5cba5b9-1aa1-4941-9e3c-d819b5fa3dbb%2Fvqw8job_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following initial value problem:
y (t) = ev()-9
y(4) = b.
It is known that the exact solution is y(t) = 9 – In(4 + e" – t).
(9.1) Euler's method is used to find the approximation of the solution for the initial value
problem on the interval [4, 7] with 6 time intervals. It is known that y2 = 3.00248. Find
an approximation for y(7) rounded to 5 decimal places. Also round your answer in each
step to 5 decimal places. Use the rounded value in the next step.
(9.2) Calculate the local error e4. Do not round answers for any intermediate steps. Give
your final answer rounded to 4 significant digits.
(9.3) Calculate the global error E4. Do not round answers for any intermediate steps.
Give your final answer rounded to 4 significant digits.
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