Problem 3. Using the system in Problem 2 to write a script to solve the following boundary value problem: y" – 2y' + y = xe“ – x, x E [0, 2] y(0) = 0, y(2) = -4, h = 0.1
Problem 3. Using the system in Problem 2 to write a script to solve the following boundary value problem: y" – 2y' + y = xe“ – x, x E [0, 2] y(0) = 0, y(2) = -4, h = 0.1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
PROBLEM 3
![Problem 2.
Using the finite difference method to solve the following boundary
value problem:
dy
dy
+p:
+ qy = f(x), y(a) = Ya, y(b) = Y6
dx?
dx
for x E [a, b]. What is the system of equations in matrix form? Assume that the interval is
broken up into N subinterval with width h and that the central difference approximation is
used to approximate the derivatives as follows
dy(x:)
Yi+1 – 2yi + Yi-1
dx?
h2
dy(x;)
Yi+1 – Yi-1
dx
2h
where p, q are constant.
Problem 3.
Using the system in Problem 2 to write a script to solve the following
boundary value problem:
y" – 2y' + y = xe" -
— в, хе [0, 2] у(0) — 0, у(2) — — 4, h%3D0.1
= -
1
The exact solution of this problem is
y(x) =
3те" + 2е* — х — 2.
Plot the numerical solution usina finite difference method and compare it with exact solution
in one figure.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe25f92a2-1c4d-41a3-af19-0cdf00d27604%2Ffaba59d3-0b29-4820-ac73-e9c3921318d4%2Fewg3bis_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2.
Using the finite difference method to solve the following boundary
value problem:
dy
dy
+p:
+ qy = f(x), y(a) = Ya, y(b) = Y6
dx?
dx
for x E [a, b]. What is the system of equations in matrix form? Assume that the interval is
broken up into N subinterval with width h and that the central difference approximation is
used to approximate the derivatives as follows
dy(x:)
Yi+1 – 2yi + Yi-1
dx?
h2
dy(x;)
Yi+1 – Yi-1
dx
2h
where p, q are constant.
Problem 3.
Using the system in Problem 2 to write a script to solve the following
boundary value problem:
y" – 2y' + y = xe" -
— в, хе [0, 2] у(0) — 0, у(2) — — 4, h%3D0.1
= -
1
The exact solution of this problem is
y(x) =
3те" + 2е* — х — 2.
Plot the numerical solution usina finite difference method and compare it with exact solution
in one figure.
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