We learned earlier that Taylor's Series gives us a reasonably good approximation to a function,
especially if we are near enough to some known starting point, and we take enough terms.
However, one of the drawbacks with Taylor's method is that you need to differentiate your
function once for each new term you want to calculate. This can be troublesome for complicated
functions, and doesn't work well in computerised modelling.
Carl Runge (pronounced "roonga") and Wilhelm Kutta (pronounced "koota") aimed to provide a
method of approximating a function without having to differentiate the original equation.
Their approach was to simulate as many steps of the Taylor's Series method but using evaluation
of the original function only
