b) Given a second order differential equation with boundary conditions drª z dz y(2)-0.008, y(8) -0.001. 1. By using finite difference method, show that the difference equation for the prob- lem above can be written as [¹2]-[2+()] + [¹] 1-1- V/+1 -0. ii. Use equation in part (i) and the boundary conditions to obtain a linear system in the form of Ayb where h= 1.5. iii. Write the Gauss-Seidel formula for the above system Ay= b found in part (i). (DO NOT SOLVE the system)
b) Given a second order differential equation with boundary conditions drª z dz y(2)-0.008, y(8) -0.001. 1. By using finite difference method, show that the difference equation for the prob- lem above can be written as [¹2]-[2+()] + [¹] 1-1- V/+1 -0. ii. Use equation in part (i) and the boundary conditions to obtain a linear system in the form of Ayb where h= 1.5. iii. Write the Gauss-Seidel formula for the above system Ay= b found in part (i). (DO NOT SOLVE the system)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![b) Given a second order differential equation
d'y 1 dy
+
z dz
with boundary conditions
y(2) 0.008, y(8)=0.001.
1. By using finite difference method, show that the difference equation for the prob-
lem above can be written as
h
[¹2]-[2+ (A)] + [¹ + 2]
1-1-
1/4
2r
V4+1 0.
ii. Use equation in part (1) 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%2F51ea7519-1b0f-4264-89e0-08b972f5e3b5%2F1aik6tt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b) Given a second order differential equation
d'y 1 dy
+
z dz
with boundary conditions
y(2) 0.008, y(8)=0.001.
1. By using finite difference method, show that the difference equation for the prob-
lem above can be written as
h
[¹2]-[2+ (A)] + [¹ + 2]
1-1-
1/4
2r
V4+1 0.
ii. Use equation in part (1) 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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