Finite Difference Examples

Numerical Analysis · Axiom Academy

EXAMPLE Computing Derivatives with Finite Differences Apply forward, backward, and central differences to approximate f'(x) Excellent work! You've computed derivative approximations using three different methods. Forward Difference: Uses f(x) and f(x+h), has O(h) error, biased toward the future Backward Difference: Uses f(x-h) and f(x), has O(h) error, biased toward the past Central Difference: Uses f(x-h) and f(x+h), has O(h²) error, much more accurate! Error Pattern: Central difference error is typically much smaller because errors cancel When computing numerical derivatives, prefer central differences for accuracy. Use forward/backward at boundaries where central isn't available.

This is the written version of the interactive lesson above. See the full Numerical Analysis course.