代做EG501V Computational Fluid Dynamics (AY 2023/24) Tutorial 4

Tutorial EG501V Computational Fluid Dynamics (AY 2023/24)

Tutorial 4. Linear systems of algebraic equations

(Q1)

a. Consider this linear system of equations

Order the four equations such that the system of equations can be solved efficiently by Gauss elimination.

b. Solve the system by Gauss elimination.

(Q2)

Given the linear system of equations  with  and  solve for  by means of an LU decomposition of [A] according to Crout’s method. Write down all steps in the solution process.

(Q3)

Consider  with  and 

Perform. 3 Gauss-Seidel iterations. Take  as the starting vector of the iteration process.

FYI: The “exact” solution is