Numerical methods for ordinary differential equations (ODEs) are used to solve initial-value problems (IVPs), which involve finding a solution to a differential equation given an initial condition.

Error and Order

Consider a numerical approximation of an exact value . Given a step size , we can denote the numerical approximation as . A numerical method is said to have an order if the error, , is as the step size .

The order of a numerical method is not related to the order of an ODE it tries to solve

Methods

First-order

Second-order

Fourth Order

See Also