An iterative algorithm for computing the effective resistance between two nodes of any resistor network

Abstract

We present an iterative method to solve for the effective resistance between two nodes of any resistor network by solving the potential at each junction. By solving for the potential at each node until the change in potential is less than ε = 1 × 10⁻⁷ from the previous iteration, we are able to obtain less than 1% deviation from the analytic solution in test resistor networks. The number of iterations needed in a square resistor grid with N nodes shows a sub-linear dependence with the size N with T ∝ N^0.797