finite difference methods

Finite difference methods are techniques used to approximate solutions to mathematical problems involving changes, such as how heat spreads or how objects move. They work by breaking a continuous problem (like a smooth curve) into small, discrete steps. Instead of calculating exact values, the method estimates how a quantity changes between these steps, allowing computers to solve complex equations numerically. Think of it as taking tiny snapshots at intervals and using them to predict the overall behavior. This approach makes analyzing real-world systems manageable when exact solutions are difficult or impossible to find analytically.