Question

Explain Runge-Kutta method
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Answer 1

The Runge–Kutta method

Slopes used by the classical Runge-Kutta method

The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method".

Let an initial value problem be specified as follows:

{\displaystyle {\frac {dy}{dt}}=f(t,y),\quad y(t_{0})=y_{0}.}

Here y is an unknown function (scalar or vector) of time t, which we would like to approximate; we are told that {\frac  {dy}{dt}}, the rate at which y changes, is a function of t and of y itself. At the initial time t_{0} the corresponding y value is y_{0}. The function f and the initial conditions t_{0},  y_{0} are given...

Answer 2

Explain Runge-Kutta method

Runge-Kutta methods are a family of iterative methods, used to approximate solutions of Ordinary Differential Equations (ODEs). Such methods use discretization to calculate the solutions in small steps. The approximation of the “next step” is calculated from the previous one, by adding s terms.