Yn+1 Yn-1 + 34. In-1 +4Jn + Jn+1], is proposed. By utilizing the model problem, y' = Xy, (a) classify this scheme in terms of consistency and order of accuracy. (b) Derive the characteristic equation and find its roots. Find the order of accuracy of this scheme by expanding the roots of the characteristic equation in powers of h. (c) Investigate the stability of this scheme for: i. A purely real. ii. A purely imaginary.
Yn+1 Yn-1 + 34. In-1 +4Jn + Jn+1], is proposed. By utilizing the model problem, y' = Xy, (a) classify this scheme in terms of consistency and order of accuracy. (b) Derive the characteristic equation and find its roots. Find the order of accuracy of this scheme by expanding the roots of the characteristic equation in powers of h. (c) Investigate the stability of this scheme for: i. A purely real. ii. A purely imaginary.
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
![The following numerical scheme:
h
Yn+1 = Yn-1 + [fn−1+4fn + fn+1],
3
is proposed. By utilizing the model problem, y' = Xy,
(a) classify this scheme in terms of consistency and order of accuracy.
(b) Derive the characteristic equation and find its roots. Find the order of accuracy
of this scheme by expanding the roots of the characteristic equation in powers of
h.
(c) Investigate the stability of this scheme for:
i. A purely real.
ii. A purely imaginary.
(d) Discuss your results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed051053-4bf3-451a-ac87-e1db40d07cdc%2F38c61cd0-7a7e-4fc2-865b-53ad83653ef2%2Fabdfoq_processed.png&w=3840&q=75)
Transcribed Image Text:The following numerical scheme:
h
Yn+1 = Yn-1 + [fn−1+4fn + fn+1],
3
is proposed. By utilizing the model problem, y' = Xy,
(a) classify this scheme in terms of consistency and order of accuracy.
(b) Derive the characteristic equation and find its roots. Find the order of accuracy
of this scheme by expanding the roots of the characteristic equation in powers of
h.
(c) Investigate the stability of this scheme for:
i. A purely real.
ii. A purely imaginary.
(d) Discuss your results.
Expert Solution
Step 1
Given: Numerical scheme and model problem
To Find :
a) Classify the scheme in terms of consistency and order of accuracy.
b) Derive the characteristic equation and also find the roots and accuracy of the scheme by expanding the roots of the characteristics equation in the power of h.
c) Investigate the stability of this scheme.
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