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Common Numerical Methods for Solving ODE's

The numerical methods for solving ordinary differential equations are methods of integrating a system of first order differential equations, since higher order ordinary differential equations can be reduced to a set of first order ODE's. For example,

n order ordinary differential can be similarly reduced to

Euler Method

The Euler method is important in concept for it points the !ay of solving ODE by marching a

small step at a time on the right"hand"side to approximate the #derivative# on the left"hand"side.

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Midpoint Method (Modified Euler Method)

The midpoint method, also $no!n as the second"order %unga"&utta method, improves the

Euler method by adding a midpoint in the step !hich increases the accuracy by one order.

Reference: http://www.efunda.com/math/num_ode/num_ode.cfm