Numerical Integration and Differential Equations

This group gathers numerical algorithms for computing an integral or solving a differential equation, including the trapezoidal rule, Simpson's rule, Romberg's method, the Runge-Kutta family of methods, predictor-corrector methods, automatic differentiation for computing exact derivatives, and iterative methods for computing mathematical constants such as pi, including the Gauss-Legendre and Chudnovsky algorithms. Their shared work is approximating a continuous mathematical quantity, an area, a derivative or the solution to a differential equation, as distinct from finding a single root or optimum, which belongs to Root-Finding and Optimization.