Any algorithms to solve an integrodifferential equation?



The following description was posted before I know the equation I
encountered is an integrodifferential equation, So now the problem is,
is there any effective codes or algorithms solving IDEs?Thanks

PS: I oftan use fortran

Hi all, I will try to make myself understood as clearly as possible,
though the problem is a little complicated, and, my English is not very
well.

the IDE has a form like this:

d P(t,k)/ d t = RHS(P,t,k)

what is weird here is that RHS(P,t,k) is a function of the concrete form
of function P(t,x) at certain step t, not merely the value of it.

inf
/
RHS(P,t,k) = | P(t,k*y)F(y) dy
/
0
given the initial conditions: P(t=0,x)=P1(x), RHS(P=P1,t=0,k)=RHS1(k)

when t=tn,
Pn(tn,x) = Pm(tm,x)+(STEPSIZE of t)*RHS(Pm,tm,x)
where m=n-1, the formula above gives the recursive procedure I should
follow in the program.

please take notice of the confusability of k and x, in the output of the
program, I want to get a series of P(t=t_end,k), k = k1,k2,k3....kp...k60, i.e.
a series of points on the output curve of function P(t=t_end, x). That
is to say, I have to an integrate different ODE for each kp.

so far, the problem is that, how to transfer the parameters effectively,
without causing confusion in the recursive procedure. For example, there
is an integration for RHS,

RHs(Pn,tn,k) calls P(tn,x), but the subroutine doing integration only
accept single value func as its parameter, so I should transform P(tn,x)
to P(x) |t=tn, where COMMON block would be used. How to make a common
block available and correct in a recursive procedure, given that the
block would change its value in different period of recursion?

I have thought of a method to crack the integration subroutine to accept
tn as a parameter, but that would destroy its stability, which I don't
prefer to.

any suggestions or comments on the algorithm? I will greatly appreciate
them since I havn't start my code yet....:) thanks



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Don't forget your dreamS
.

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