cmlyneis

12-16-2012, 11:45 PM

Trying to find an IMSL solver for a set of coupled ordinary differential equations of the form

(d/dt)(An)=iBn(t)An+SUM (Tnq(z)Aq +Tn,q+1Aq+1......where An(0)=1, Aq(0)=0 with q not equal n

where i is sqrt of -1 so the functions have complex numbers in them.

The routines IVPRK, IVMRK,IVPAG are set up for first order ordinary differential equation with initial values, but

there is no mention of whether these can deal with equations with complex coefficients.

The basic equation form is

y1'=a(t)y1+b(t)y2+c(t)y3 ......

y2'=d(t)y2+e(t)y1+f(t)y3 ....

where typically a(t),b(t)...are complex and y1(0)=1, y2(0)=0,y(0)=0....

and the goal is to find values of y1,y2--as a function of t.

None of the examples for these routine mention complex coefficients. From the literature I know these equations can be

solve by a Runge Kutta integration. This is related to mode conversion in over moded circular microwave waveguides.

Any suggestions would be welcome.

Claude

(d/dt)(An)=iBn(t)An+SUM (Tnq(z)Aq +Tn,q+1Aq+1......where An(0)=1, Aq(0)=0 with q not equal n

where i is sqrt of -1 so the functions have complex numbers in them.

The routines IVPRK, IVMRK,IVPAG are set up for first order ordinary differential equation with initial values, but

there is no mention of whether these can deal with equations with complex coefficients.

The basic equation form is

y1'=a(t)y1+b(t)y2+c(t)y3 ......

y2'=d(t)y2+e(t)y1+f(t)y3 ....

where typically a(t),b(t)...are complex and y1(0)=1, y2(0)=0,y(0)=0....

and the goal is to find values of y1,y2--as a function of t.

None of the examples for these routine mention complex coefficients. From the literature I know these equations can be

solve by a Runge Kutta integration. This is related to mode conversion in over moded circular microwave waveguides.

Any suggestions would be welcome.

Claude