3) a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b) Consider the second-order truncation error (0 (Ax)2) with the step size (-Ax ) and then, obtain a finite difference approximation for the first-order derivative of U(x, t) respect x (Ux(x, t)). c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax) then, subtract them and finally obtain a finite difference approximation for the first-order derivative of U respect x (Ux(x, t)). d) Consider the fourth-order truncation error (0(Ax )4) with the step size Ax and also (-Ax ) then, add them and finally obtain a finite difference approximation for the second-order derivative of U respect x (Uxx(x, t)).
3) a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b) Consider the second-order truncation error (0 (Ax)2) with the step size (-Ax ) and then, obtain a finite difference approximation for the first-order derivative of U(x, t) respect x (Ux(x, t)). c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax) then, subtract them and finally obtain a finite difference approximation for the first-order derivative of U respect x (Ux(x, t)). d) Consider the fourth-order truncation error (0(Ax )4) with the step size Ax and also (-Ax ) then, add them and finally obtain a finite difference approximation for the second-order derivative of U respect x (Uxx(x, t)).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
Related questions
Question
![3)
a) Use the Taylor theorem for function U(x, t) with the step size(−Ax ) (t, is
held cons.
b) Consider the second-order truncation error (0(Ax )²) with the step size
(-Ax ) and then, obtain a finite difference approximation for the first-order
derivative of U(x, t) respect x (Ux(x, t)) .
c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and
also (-Ax) then, subtract them and finally obtain a finite difference
approximation for the first-order derivative of U respect x (Ux(x, t)).
d) Consider the fourth-order truncation error (0(Ax )4) with the step size
Ax and also (-Ax) then, add them and finally obtain a finite difference
approximation for the second-order derivative of U respect x (Uxx (x, t)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1aa5ff01-58a5-4f17-87cd-234e60ad4800%2Fd89dfa2f-bee9-4912-88aa-1e756163f5a0%2F4e8r1ld_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3)
a) Use the Taylor theorem for function U(x, t) with the step size(−Ax ) (t, is
held cons.
b) Consider the second-order truncation error (0(Ax )²) with the step size
(-Ax ) and then, obtain a finite difference approximation for the first-order
derivative of U(x, t) respect x (Ux(x, t)) .
c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and
also (-Ax) then, subtract them and finally obtain a finite difference
approximation for the first-order derivative of U respect x (Ux(x, t)).
d) Consider the fourth-order truncation error (0(Ax )4) with the step size
Ax and also (-Ax) then, add them and finally obtain a finite difference
approximation for the second-order derivative of U respect x (Uxx (x, t)).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Functions and Change: A Modeling Approach to Coll…](https://www.bartleby.com/isbn_cover_images/9781337111348/9781337111348_smallCoverImage.gif)
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Functions and Change: A Modeling Approach to Coll…](https://www.bartleby.com/isbn_cover_images/9781337111348/9781337111348_smallCoverImage.gif)
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage