ODRKG/ODRK4/ODRK2/ODRK1

DCL:MATH 2:ODELIB: Ordinary Differential Equation (Runge-Kutta Method): Explanation of Subroutines

3.3.1 ODRKG/ODRK4/ODRK2/ODRK1

1.

Function

Performs a one-step integration using the given step width following a specific algorithm. The algorithms for integration are: the Runge-Kutta-Gill method (ODRKGODRK4), the 2nd-order Runge-Kutta method (ODRK2), and the 1st-order Runge-Kutta (Euler) method (ODRK1).

2.

Call

CALL ODRKG(N,FCN,T,DT,X,DX,XOUT,WORK)
CALL ODRK4(N,FCN,T,DT,X,DX,XOUT,WORK)
CALL ODRK2(N,FCN,T,DT,X,DX,XOUT,WORK)
CALL ODRK1(N,FCN,T,DT,X,DX,XOUT,WORK)

3.

Explanation of Parameters

N (I) Number of the variables of integration (or integrands) (i)

FCN Name of procedure Name of subroutine that calculates DX.

T (R) Value of independent variable t. (i)

DT (R) Step width of integration. (i)

X R(N) Value of variable of integration at t=T. (i)

DX R(N) Value of derivative of the variable of integration at t=T. (i) In ODRKG, the value of DX is not retained.

XOUT R(N) Value of variable of integration at t =T+DT. (i) The same variable as X may be specified as the floating-point variable.

WORK R(N,M) Working variable. M=3 (for ODRK4) or 1 (for other routines).

4.

Notes

(a): FCN is provided by the user in the form of a subroutine according to the following format:
SUBROUTINE FCN(N,T,X,DX).

`N`	`(I)`	Number of the variables of integration (or integrands) (i)
`FCN`	Name of procedure	Name of subroutine that calculates `DX`.
`T`	`(R)`	Value of independent variable t. (i)
`DT`	`(R)`	Step width of integration. (i)
`X`	`R(N)`	Value of variable of integration at t=T. (i)
`DX`	`R(N)`	Value of derivative of the variable of integration at t=T. (i) In `ODRKG`, the value of `DX` is not retained.
`XOUT`	`R(N)`	Value of variable of integration at t =T+DT. (i) The same variable as `X` may be specified as the floating-point variable.
`WORK`	`R(N,M)`	Working variable. M=3 (for `ODRK4`) or 1 (for other routines).