I was wondering if anyone could recommend a good book or resource on numerical methods for solving integro-differential equations? Of course I am familiar with the methods for solving ODEs and PDEs numerically, so no problem there. But I don't have any frame of reference on the stability of numerical schemes when solving integro-differential equations, such as the Smoluchowski coagulation equation, or Volterra integro-differential equations. I can try to drop in some numerical integration routine into the ODE solver, but I am just not sure under what conditions this gives me a good solution versus accumulating errors over time.

I looked at one book by Lakshmikantham called Theory of Integro-Differential Equations, but I did not see any mention of numerical schemes. I will continue to look over that book, but if anyone knows of a good reference that would be very helpful.



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