The Fourth Order Runge Kutta Method

The Runge-Kutta methods for numerical solution of the differential equation dy/dx = F{x, y) involve, in effect, the evaluation of the differential function at intermediate points between x„ and xn+\. The value of y„+\ is obtained by appropriate summation of the intermediate terms in a single equation. The most widely used Runge-Kutta formula involves terms evaluated at x„, xn+Ax/2 and x„+ax- The fourth-order Runge-Kutta equations for dy/dx = F{x, y) are

Ax T

If more than one variable appears in the expression, then each is corrected by using its own set of T\ to r4 terms.

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