Two-dimensional transport equation as Fredholm integral equation

The transport equation has many applications in various fields of science and engineering. In this paper we shown that we can transform a transport equation in two-dimensional case into a Fredholm integral equation of the second kind with a compact integral operator for the angular flux by using the Sumudu transform.

Research highlights
► Two dimensional transport equation was transformed into a Fredholm integral equation.
► The subcritical case was investigated.
► Tau method can be applied to solve numerically the obtained equation