Applying the Successive Over-relaxation Method to a Real World Problems

Abstract

Solving a system of equations by 𝐴𝐴𝐴𝐴 = 𝑏𝑏, where A is a 𝑛𝑛×𝑛𝑛 matrix and b and 𝑛𝑛×1 vector, can sometime be a daunting task because solving for x can be difficult. If you were given an algorithm that was efficient, that’s great! What if you could make it solve the problem even faster? That’s even better. We will first take a look at establishing the basics of the successive over-relaxation method (SOR for short), then we’ll look at a real-world problem we applied the SOR method to, solving the heat-equation when a constant boundary temperature is applied to a flat plate.