25.14.3. Successive Over-Relaxation (SOR)

Try these first

1. 1.

   Define Successive Over-Relaxation (SOR).

   Hint

   Think about its relationship to the Gauss-Seidel method.

2. 2.

   What is the relaxation parameter ω used for?

   Hint

   Consider how it affects convergence.

3. 3.

   What does SOR stand for?

   • Simple Over-Relaxation
   • Successive Over-Relaxation
   • Simplicity in Over-Relaxation

   Hint

   Think about what this method improves upon.

4. 4.

   True or False: The relaxation parameter ω can exceed 1.

   • True
   • False

   Hint

   Remember what effect different ω values have.

5. 5.

   Given a system of linear equations, derive a SOR iteration formula taking ω = 1.5.

   Hint

   Work through the Gauss-Seidel method steps first to build your SOR formulation.

6. 6.

   Formulate a strategy for determining the best relaxation parameter for a specific system of non-linear equations.

   Hint

   Use graphical representation to visualize convergence speed with varying ω values.