The convergence analysis for sixth-order methods for solving discrete-ordinates slab transport equations

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Abstract
Functional analytic methods, employing the CollectiVely compact operator approximation theory of P.M. Anselone, are utilized to study the convergence properties of four improvements to the rather promising quadratic method of Gopinath, Natarajan, and Sundararaman [Nucl. Sci. Eng. 75 (1980), 181-184] for effecting slab transport calculations. This method displays a global discretization error of order four; our alterations too possess global discretization errors of order four, but display superconvergence phenomena in that the discretization errors in computed cell-edge fluxes are of order six. The stability of our methods results from applying Anselone's theory of sequences of collectively compact operators. A numerical example is provided which shows that our asymptotic convergence rates are observed on rather coarse meshes.