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
![You want to find a numerical solution to
dy
= -0.21 (1+y)?
dx
with y(0)=1.
You want to use the implicit Simpson scheme (Milne's method)
n-
to estimate the solution at x=0.5 using a step length h= 0.25. To do this you need an
estimate of y, ·
Use Euler's explicit method to estimate y, and as a predictor for the above scheme
before taking three iterations of the implicit scheme to find and estimate of y2.
Give all your answers to 5 decimal places (no more and no less).
The estimate of y, is
The first estimate of y, using the predictor is
Using Simpson's method, the estimate of y, after 3 iterations of the scheme is y, =
Find the true solution of the differential equation and calculate the correct value at
x=0.5:
y(0.5) =
The size of the error of this first estimate =
In order to improve the accuracy of your numerical estimate you are to use a power
series expansion of y(x) to estimate y,. Find the expansion up to the x term, filling
in the coefficients below:
y(x) =
+
x2 +
+
The estimate of y, using the power series expansion up to x* is
The second estimate of y, , again using the Euler forward difference scheme as a
predictor and three iterations of the Simpson scheme, is y, =
The size of the error of your second estimate =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd731cc0a-d3d2-4354-9f84-66b79a232ce6%2Fe26514a1-5348-491d-b307-e288f6acf56e%2Fnj65uoo_processed.png&w=3840&q=75)
Transcribed Image Text:You want to find a numerical solution to
dy
= -0.21 (1+y)?
dx
with y(0)=1.
You want to use the implicit Simpson scheme (Milne's method)
n-
to estimate the solution at x=0.5 using a step length h= 0.25. To do this you need an
estimate of y, ·
Use Euler's explicit method to estimate y, and as a predictor for the above scheme
before taking three iterations of the implicit scheme to find and estimate of y2.
Give all your answers to 5 decimal places (no more and no less).
The estimate of y, is
The first estimate of y, using the predictor is
Using Simpson's method, the estimate of y, after 3 iterations of the scheme is y, =
Find the true solution of the differential equation and calculate the correct value at
x=0.5:
y(0.5) =
The size of the error of this first estimate =
In order to improve the accuracy of your numerical estimate you are to use a power
series expansion of y(x) to estimate y,. Find the expansion up to the x term, filling
in the coefficients below:
y(x) =
+
x2 +
+
The estimate of y, using the power series expansion up to x* is
The second estimate of y, , again using the Euler forward difference scheme as a
predictor and three iterations of the Simpson scheme, is y, =
The size of the error of your second estimate =
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 13 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)