On projection and variational methods in kinetic theory

In this paper complementary variational and bivariational principles for obtaining bounds to functionals of solutions of Fredholm integral equations are coupled to an appropriate Ritz system of orthonormal coordinate functions. It is shown that these general principles may be expressed in terms of the elements of the classical projection system. Applications are made to the rarefied gas problems of Couette, Poiseuille and thermal creep flows, and numerical results are reported. Particular attention is given to the numerical precision and stability of the calculations.