b) Given a second order differential equation d'y 1 dy + d.x² x dx with boundary conditions. Y x² = 0, y(2) = 0.008, y (8) = 0.001. i. By using finite difference method, show that the difference equation for the prob- lem above can be written as h h [¹ - 2] -- [2 + ( ² ) ] × - [¹ + 2 ] Yi-1 2+ Yi + Yi+1 2xi 2xi = 0. = ii. Use equation in part (i) and the boundary conditions to obtain a linear system in the form of Ay = b where h = 1.5. iii. Write the Gauss-Seidel formula for the above system Ay = b found in part (ii). (DO NOT SOLVE the system)
b) Given a second order differential equation d'y 1 dy + d.x² x dx with boundary conditions. Y x² = 0, y(2) = 0.008, y (8) = 0.001. i. By using finite difference method, show that the difference equation for the prob- lem above can be written as h h [¹ - 2] -- [2 + ( ² ) ] × - [¹ + 2 ] Yi-1 2+ Yi + Yi+1 2xi 2xi = 0. = ii. Use equation in part (i) and the boundary conditions to obtain a linear system in the form of Ay = b where h = 1.5. iii. Write the Gauss-Seidel formula for the above system Ay = b found in part (ii). (DO NOT SOLVE the system)
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
![b) Given a second order differential equation
1 dy
x dx
with boundary conditions
d'y
dx²
+
Y
x²
=
0,
y (2) = 0.008, y(8) = 0.001.
i. By using finite difference method, show that the difference equation for the prob-
lem above can be written as
h
h
[¹ – 2 ] × ₁ - [2 + ( 2 ) ] × + [¹ + 2 ]
Yi-1
Yi
2x₂
2xi
Yi+1 = 0.
=
ii. Use equation in part (i) and the boundary conditions to obtain a linear system in
the form of Ay = b where h = 1.5.
iii. Write the Gauss-Seidel formula for the above system Ay = b found in part (ii).
(DO NOT SOLVE the system)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa326aca-745f-410c-a63e-6ad225fdb3f7%2F878e50dd-5a83-45ac-b8fc-58a58d682838%2Fcl54mka_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b) Given a second order differential equation
1 dy
x dx
with boundary conditions
d'y
dx²
+
Y
x²
=
0,
y (2) = 0.008, y(8) = 0.001.
i. By using finite difference method, show that the difference equation for the prob-
lem above can be written as
h
h
[¹ – 2 ] × ₁ - [2 + ( 2 ) ] × + [¹ + 2 ]
Yi-1
Yi
2x₂
2xi
Yi+1 = 0.
=
ii. Use equation in part (i) and the boundary conditions to obtain a linear system in
the form of Ay = b where h = 1.5.
iii. Write the Gauss-Seidel formula for the above system Ay = b found in part (ii).
(DO NOT SOLVE the system)
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