Eigenvalue Correlation Problem For A Transport Equation In Slab Geometry

The transport equation is a mathematical model for studying the law of macroscopic transport caused by the integration of microscopic effects produced by the movement of particles.It is a very complex form of a equation that contains both integral and differential.The migration equation can be divided into: half space,flat plate,sphere,cylinder,convex;divided by time: steady state,dynamic;divided according to the scattering direction: isotropic scattering,anisotropic scattering;there are also many types of division by reflection boundary conditions,etc.It is one of the main contents of the transport equation theory to solve the numerical solution of the transport equation according to different types.Analyzing the eigenvalue problem of the transport equation and studying the convergence of the transport equation operators is one of the main ways to find the numerical solution of the transport equation in Lp(1 < p < ?)space.This provides many innovative ideas for the study of space theory,equation theory and operator theory.The objective of this thesis is to research the problem of the eigenvalue of the anisotropic scattering transport equation in slab geometry.Different from traditional methods,this paper utilizes the mean projection method to deal with the eigenvalue of dynamic problems.By using of the mean projection method to obtain the approximate eigenvalues,we theoretically prove the convergence of eigenvalues and eigenvectors.Furthermore,we obtained higher convergence order,and the convergence rate of approximate eigenvalues and eigenvectors is improved.