RK4
Syntax | Return Value | Arguments | Keywords | Examples | Version History | See Also
The RK4 function uses the fourth-order Runge-Kutta method to advance a solution to a system of ordinary differential equations one time-step H, given values for the variables Y and their derivatives Dydx known at X.
RK4 is based on the routine rk4 described in section 16.1 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press, and is used by permission.
Syntax
Result = RK4( Y, Dydx, X, H, Derivs [, /DOUBLE] )
Return Value
Returns the integrations of the ordinary differential equations.
Arguments
Y
A vector of values for Y at X
Note
If RK4 is complex then only the real part is used for the computation.
Dydx
A vector of derivatives for Y at X.
X
A scalar value for the initial condition.
H
A scalar value giving interval length or step size.
Derivs
A scalar string specifying the name of a user-supplied IDL function that calculates the values of the derivatives Dydx at X. This function must accept two arguments: A scalar floating value X, and one n-element vector Y. It must return an n-element vector result.
For example, suppose the values of the derivatives are defined by the following relations:
dy0 / dx = –0.5y0, dy1 / dx = 4.0 – 0.3y1 – 0.1y0
We can write a function DIFFERENTIAL to express these relationships in the IDL language:
Keywords
DOUBLE
Set this keyword to force the computation to be done in double-precision arithmetic.
Examples
To integrate the example system of differential equations for one time step, H:
IDL prints:
This is the exact solution vector to five-decimal precision.
Version History
