# Fredholm integral equation of the second kind with kernel containing Bessel and Struve functions

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ep on 25 Aug 2014
Commented: Star Strider on 27 Aug 2014
I need to solve this Fredholm integral equation of the second kind:
f[s]+integrate[f[t] K[s,t],{t,0,1}]=s
where 0<=s<=1.
The kernel is:
K[s,t]=(a/2)*(BesselJ[1,a*(s+t)]-BesselJ[1,a*Abs[s-t]]-i*StruveH[1,a*(s+t)]+i*StruveH[1,a*Abs(s-t)])
where a: real, i: imaginary unit.
The coding is from Mathematica (Matlab does not have a Struve function in its library like Mathematica does). I use this: http://www.mathworks.com/matlabcentral/fileexchange/19456-fredholm-integral-equations program to solve the integral equation but I have a problem with respect to the kernel. I haven't found how to solve symbolically the Struve function. For the Bessel one I use the Symbolic Math Toolbox and the besselj function but for the Struve one the only algorithms I have found online are ones that solve the function for a number (real,complex etc but not for a symbol). The kernel needs to be a function of s and t in order to use it in the integral. Could anyone please help me figure it out?

Star Strider on 25 Aug 2014
I’m not familiar with Struve functions, but in my search to learn something about them, I discovered this File Exchange contribution: Struve functions. See if it does what you want.
Star Strider on 27 Aug 2014
The only option I can consider in that instance is to keep everything symbolic and code your own Struve functions. This should not be a problem unless you have many to integrate. The Symbolic Math Toolbox is not optimal for any sort of recursion.