Methods of successive approximation

Mathematical methods relating to successive approximation include the following:

• Babylonian method, for finding square roots of numbers
• Fixed-point iteration
• Means of finding zeros of functions:
  • Halley's method
  • Newton's method
• Differential-equation matters:
  • Picard–Lindelöf theorem, on existence of solutions of differential equations
  • Runge–Kutta methods, for numerical solution of differential equations