This paper presents the application of isogeometric analysis (IGA) to the spatial discretisation
of the multi-group, self-adjoint angular flux (SAAF) form of the neutron transport equation with
a discrete ordinate (SN) angular discretisation. The IGA spatial discretisation is based upon
non-uniform rational B-spline (NURBS) basis functions for both the test and trial functions. In
addition a source iteration compatible maximum principle is used to derive the IGA spatially
discretised SAAF equation. It is demonstrated that this maximum principle is mathematically
equivalent to the weak form of the SAAF equation. The rate of convergence of the IGA spatial discretisation of the SAAF equation is analysed using a method of manufactured solutions
(MMS) verification test case. The results of several nuclear reactor physics verification benchmark test cases are analysed. This analysis demonstrates that for higher-order basis functions,
and for the same number of degrees of freedom, the FE based spatial discretisation methods are
numerically less accurate than IGA methods. The difference in numerical accuracy between the
IGA and FE methods is shown to be because of the higher-order continuity of NURBS basis
functions within a NURBS patch as well as the preservation of both the volume and surface
area throughout the solution domain within the IGA spatial discretisation. Finally, the numerical
results of applying the IGA SAAF method to the OECD/NEA, seven-group, two-dimensional
C5G7 quarter core nuclear reactor physics verification benchmark test case are presented. The
results, from this verification benchmark test case, are shown to be in good agreement with solutions of the first-order form as well as the second-order even-parity form of the neutron transport
equation for the same order of discrete ordinate (SN) angular approximation.