Consider a system of equations where the ith equation is aiΦi=bi Φi+1+ciΦi-1+di. While solving this system using Thomas algorithm, we get Φi=PiΦi+1+Qi. What are P1 and Q1?

\(P_1=\frac{d_1}{a_1-c_1};Q_1=\frac{b_1}{a_1-c_1}\)

\(P_1=\frac{b_1}{a_1-c_1};Q_1=\frac{d_1}{a_1-c_1}\)

\(P_1=\frac{d_1}{a_1};Q_1=\frac{b_1}{a_1}\)

\(P_1=\frac{b_1}{a_1};Q_1=\frac{d_1}{a_1}\)

Consider a system of equations where the ith equation is ai Φi=bi Φ(i+1)+ci Φ(i+1)+di. While solving this system using Thomas algorithm, we get Φi=Pi Φ(i+1)+Qi. What are Pi and Qi?

\(P_i=\frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}};Q_i=\frac{b_i}{a_i-c_i P_{i-1}}\)

\(P_i=\frac{b_i}{a_i-c_i P_{i-1}};Q_i=\frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}}\)

\(P_i=\frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}};Q_i=\frac{d_i}{a_i-c_i P_{i-1}}\)

\(P_i=\frac{d_i}{a_i-c_i P_{i-1}};Q_i=\frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}}\)

Explore topic-wise MCQs in Computational Fluid Dynamics Questions and Answers.

This section includes 6 Mcqs, each offering curated multiple-choice questions to sharpen your Computational Fluid Dynamics Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.

1.	Consider a system of equations where the ith equation is aiΦi=bi Φi+1+ciΦi-1+di. While solving this system using Thomas algorithm, we get Φi=PiΦi+1+Qi. What are P1 and Q1?
A.	\(P_1=\frac{d_1}{a_1-c_1};Q_1=\frac{b_1}{a_1-c_1}\)
B.	\(P_1=\frac{b_1}{a_1-c_1};Q_1=\frac{d_1}{a_1-c_1}\)
C.	\(P_1=\frac{d_1}{a_1};Q_1=\frac{b_1}{a_1}\)
D.	\(P_1=\frac{b_1}{a_1};Q_1=\frac{d_1}{a_1}\)
Answer» E.

Discussion

2.	After finding all the values of Pi and Qi, in which order are the values of Φi found?
A.	Forward
B.	Simultaneously
C.	Backwards
D.	Depends on the problem
Answer» D. Depends on the problem

Discussion

3.	While solving a system of equations with the Thomas algorithm, in which order are the values of Pi and Qi found?
A.	Backwards
B.	Forward
C.	Simultaneously
D.	Depends on the problem
Answer» C. Simultaneously

Discussion

4.	Using the Thomas algorithm, if the ith unknown is Φi=Pi Φi+1+Qi. what is the last unknown value ΦN equal to?
A.	0
B.	PN
C.	QN
D.	1
Answer» D. 1

Discussion

5.	Let the ith equation of a system of n equations be aiΦi=bi Φi+1+ciΦi-1+di. Which of these is correct?
A.	cN=0; bN=0
B.	cN=0; b1=0
C.	c1=0; bN=0
D.	c1=0; b1=0
Answer» D. c1=0; b1=0

Discussion

6.	Consider a system of equations where the ith equation is ai Φi=bi Φ(i+1)+ci Φ(i+1)+di. While solving this system using Thomas algorithm, we get Φi=Pi Φ(i+1)+Qi. What are Pi and Qi?
A.	\(P_i=\frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}};Q_i=\frac{b_i}{a_i-c_i P_{i-1}}\)
B.	\(P_i=\frac{b_i}{a_i-c_i P_{i-1}};Q_i=\frac{c_i Q_{i-1}+d_i}{a_i-c_i P_{i-1}}\)
C.	\(P_i=\frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}};Q_i=\frac{d_i}{a_i-c_i P_{i-1}}\)
D.	\(P_i=\frac{d_i}{a_i-c_i P_{i-1}};Q_i=\frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}}\)
Answer» C. \(P_i=\frac{c_i Q_{i-1}+b_i}{a_i-c_i P_{i-1}};Q_i=\frac{d_i}{a_i-c_i P_{i-1}}\)

Discussion

Explore topic-wise MCQs in Computational Fluid Dynamics Questions and Answers.

Consider a system of equations where the ith equation is aiΦi=bi Φi+1+ciΦi-1+di. While solving this system using Thomas algorithm, we get Φi=PiΦi+1+Qi. What are P1 and Q1?

After finding all the values of Pi and Qi, in which order are the values of Φi found?

While solving a system of equations with the Thomas algorithm, in which order are the values of Pi and Qi found?

Using the Thomas algorithm, if the ith unknown is Φi=Pi Φi+1+Qi. what is the last unknown value ΦN equal to?

Let the ith equation of a system of n equations be aiΦi=bi Φi+1+ciΦi-1+di. Which of these is correct?

Consider a system of equations where the ith equation is ai Φi=bi Φ(i+1)+ci Φ(i+1)+di. While solving this system using Thomas algorithm, we get Φi=Pi Φ(i+1)+Qi. What are Pi and Qi?