A Discrete Ordinates Method Of Transport Equation With Reflection Noundary Conditions In The Space Of L~p

The transport equation is a complex equation that contains differential and integral forms.A mathematical model mainly used to study the law of macroscopic migration phenomena caused by the combination of microscopic effects produced by particle motion in bulk materials.Because it involves many applied disciplines such as physics,biology,chemistry,etc.,many practical problems can be solved by the transfer equation,so more and more scholars are interested in research on the transport equation.Divided by region,the transport equation can be divided into half space,flat plate,sphere,convex body,and cylinder;according to the scattering direction,it can be divided into isotropic scattering and anisotropic scattering;according to time,it can be divided into steady state and dynamic;according to the boundary conditions,there are also different division methods,the problem of solving the numerical solution of the transport equation according to different types is an im-portant content of the theoretical research of the transport equation.Nowadays,the asymptotic behavior of the solution of the transport equation and the spectral analysis of the transport operator have become the content of discussion by many scholars.Solve the eigenvalues of the transport equation in the Lp space,discussing the convergence and boundedness of the transport equation operator,is an effective method for solving the numerical solution of the transport equation.The research in this direction provides new ideas for the research of equation theory and operator theory and has certain research value.In this paper,in the Lp space,the transport equation of the plate geometry with reflection boundary conditions is studied,a new mean projection method is given,which satisfies the norm convergence,and discuss the convergence and error analysis of the eigenvalues and eigenfunctions of the transport equation,the higher rate of convergence is obtained.