Numerical methods for ordinary differential equations

Illustration of numerical integration for the differential equation
  Blue: Euler method
  Green: Midpoint method
  Red: Exact solution: .
The step size is .
The same illustration for The midpoint method converges faster than the Euler method, as .

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals.

Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the solution.

Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics.[1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.

  1. ^ Chicone, C. (2006). Ordinary differential equations with applications (Vol. 34). Springer Science & Business Media.