Question

Consider a system of equations where the i^th 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) \(P_1=\frac{b_1}{a_1};Q_1=\frac{d_1}{a_1}\)

This question was addressed to me during an online exam.

This intriguing question comes from Discretization Aspects topic in chapter Basic Aspects of Discretization, Grid Generation with Appropriate Transformation of Computational Fluid Dynamics

Answer 1

The correct choice is (d) \(P_1=\frac{b_1}{a_1};Q_1=\frac{d_1}{a_1}\)

Best explanation: In general,

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

As c1=0,

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