Quadrature Methods With High Accuracy For Solving Eigenvalue Problems Of The Transport Equation

The eigenvalue problems of the transport equation is an important area in reactor physics astronomical physics and radiation transfer.For the complexity of the transport equation ,It's hard to be analytic solved ,except for special conditions. Many numerical methods are widely applied in the study of transport in practical problems.By means of the compact operators ,the eigenvalue problems of transport equation are transformed into eigenvalue problems of weakly singular integral operators. Applying Side's quadrature rules ,we present the quadrature methods with high accuracy for solving eigenvalue problems of the transport equation. An asymptotic expansion of the errors with O(h3) is shown. Therefore , by using extrapolation we can improve the accuracy order of approximations.In the end ,we derive a posterior estimate .Numerical results show that we can get satisfied accuracy .Some significant results have been...