Runge kutta method.

The Taylor's series method of solving differential equations numerically is restricted by the labour involved in finding the higher order derivatives. However there is a class of methods known as Runge-kutta methods which do not require the calculations of higher order derivatives and give greater accuracy. The Runge kutta formulae possess the advantage of requiring only the function values at some selected points. These methods agree with Taylor's series solution upto the term hⁿ when n differs from method and is called the order of that method.