Examples for

# Numerical Analysis

The field of numerical analysis focuses on algorithms that use numerical approximation for the problems of mathematical analysis. Wolfram|Alpha provides algorithms for solving integrals, differential equations and the roots of equations through a variety of numerical methods. Compare different methods for accuracy and speed. Use fine control over such parameters as step size or starting point.

Compute roots using specific starting points, precisions and numerical methods.

#### Find the roots of an equation using Newton's method:

#### Find the roots of an equation using the secant method:

#### Compute the nth root of a number using the bisection method:

Compute solutions to ordinary differential equations using numerical methods, such as Euler's method, the midpoint method and the Runge–Kutta methods.

#### Solve an ODE using a specified numerical method:

#### Specify an adaptive method:

Use numerical integration methods, such as the trapezoidal rule, to solve integrals.