General Integral Types

The integral equations that we have been working with in this chapter are part of a larger class of equations known as Fredholm integrals. There are Fredholm integrals of the first and second kind that take the general form of Eq. (21.22) and Eq. (21.23).

Equation 21.22

Equation 21.23

The quantity K ( t , s ) is known as the kernel. The equations used in the examples in this chapter have been Fredholm integrals of the first kind with K ( t , s ) = 1. Another important type of integral is a Volterra integral that is similar to a Fredholm integral of the first kind except the upper integration limit is t . We won't implement methods to solve general Fredholm or Volterra integrals, but they are typically solved using Gaussian quadrature methods described in the previous section.