# Numerical packages to solve Volterra integral equations

I am looking for numerical packages (ideally Python) to solve second kind Volterra integral equations, such as

$$u(t)=g(t)+\int_0^tK(t,s)u(s) ds$$

or Volterra-Fredholm integral equations

$$u(x,t)=g(t,x)+c\int_0^t\int_\Omega K(t,s,x,\xi)u(s,\xi) d\xi ds$$

Are there any callable functions in Python to solve such equations? if not, are there any standard algorithm to solve such equations?

• For the most general case you can use scipy.integrate to solve integral equations. If the kernel is exponential maybe you can use laplace transforms or FFTs. – jadelord May 16 '18 at 16:16