(2) You've used a numerical method with second-order global error to estimate the value of a solution of a differential equation, and using 4 time steps you've got an error not exceeding 0.25. How many times must you halve the step size to be sure the error is less than 0.0001? How does the answer change if the method were fifth-order instead?
(2) You've used a numerical method with second-order global error to estimate the value of a solution of a differential equation, and using 4 time steps you've got an error not exceeding 0.25. How many times must you halve the step size to be sure the error is less than 0.0001? How does the answer change if the method were fifth-order instead?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:(2) You've used a numerical method with second-order global error to estimate the
value of a solution of a differential equation, and using 4 time steps you've got
an error not exceeding 0.25. How many times must you halve the step size to be
sure the error is less than 0.0001? How does the answer change if the method
were fifth-order instead?
Expert Solution
Step 1
Sol:-
If the numerical method used has a second-order global error, we know that the error decreases quadratically with the step size, h. Therefore, if we halve the step size, the error should decrease by a factor of 4.
Let E(h) be the error associated with a step size h. If using a step size h results in an error not exceeding 0.25, then we have E(h) ≤ 0.25.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
