finite-difference method

The finite-difference method is a numerical technique used to approximate solutions to mathematical equations, especially those involving change over space or time. It works by replacing continuous problems, like how a temperature varies across a surface, with a grid of discrete points. The changes between these points are calculated using differences, akin to small steps, allowing complex equations to be solved computationally. This method is widely used in engineering and physics to simulate phenomena such as heat transfer, fluid flow, and structural analysis when exact solutions are difficult or impossible to obtain analytically.