Numerical results for the transport equation with strongly anisotropic scattering in a slab

• We solve numerically the strongly anisotropic transport equation using techniques of integral operators.
• We present numerical results for one dimensional transport equation near criticality.
• We present numerical results for the transport equation with forward–backward-anisotropic scattering kernel.
• The existence theory is obtained with analytical estimates on the involved operator.

In this work we solve the transport equation with strongly anisotropic scattering, i.e., with a forward–backward-anisotropic kernel. We treat the problem by finding an integral representation to the solution, which we then project to a finite dimensional space. We verify numerically the robustness of the techniques we develop by performing calculations for several cases found in the literature. Then we obtain new numerical results for the transport equation with strongly anisotropic scattering when the kernel has more than two terms. Our simulations allows us to obtain the total intensity, the total flux, the dominant eigenvalue and the critical thickness with precision to at least five digits. These simulations indicate that adding third and fourth kernel terms contributes to about 1% in the studied cases.