4. Taylor method of order three is given by Yi+1 = Y; +hT(³) (t₁, Y;), where T(³) (t₁, Y;) = f (t¡‚ Yi) + h h² (ti, Yi) + / / f '(t₁, Y) + h ¯¯ ƒ' 3! f " (ti, Yi) Write out this method's formula when it is applied to the IVP: y' = -y + sin t. (The formula expression should have no f, f', or f", it should only involves t, h and y. Do not carry out the actual calculations)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
4. Taylor method of order three is given by
h
Yi+1 = Y¡ + hT (³) (t₁, Y;), where T(³) (t¡‚, Y;) = ƒ (t¡‚Y;) + − ƒ' (t¡‚Y;) +
h²
- ƒ"(ti, Y;)
3!
Write out this method's formula when it is applied to the IVP: y' = -y + sin t.
(The formula expression should have no f, f', or f", it should only involves t, h and y. Do not carry out
the actual calculations)
Transcribed Image Text:4. Taylor method of order three is given by h Yi+1 = Y¡ + hT (³) (t₁, Y;), where T(³) (t¡‚, Y;) = ƒ (t¡‚Y;) + − ƒ' (t¡‚Y;) + h² - ƒ"(ti, Y;) 3! Write out this method's formula when it is applied to the IVP: y' = -y + sin t. (The formula expression should have no f, f', or f", it should only involves t, h and y. Do not carry out the actual calculations)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,