Finite Difference Method
A numerical method for solving differential equations by approximating derivatives with finite difference quotients on a discretized grid.
Governing formula
f'(x) ≈ (f(x + h) - f(x - h)) / (2 h), f''(x) ≈ (f(x+h) - 2f(x) + f(x-h)) / h²
SI unit
Grid Discretization Method
In depth
Replaces continuous derivatives with Taylor series difference approximations on a spatial grid. Converts differential equations into explicit or implicit matrix algebraic systems.
Examples in the real world
Discretizing the 2D Poisson equation ∇²u = f on a rectangular grid using 5-point stencil operators.