PREDICTOR-CORRECTOR SCHEME FOR DIGITAL SOLUTION OF THE PARTIAL DIFFERENTIAL EQUATION FOR ATMOSPHERIC DIFFUSION FROM A LINE SOURCE.

摘要

The purpose of the report is to extend the range and accuracy of our computer program for the predictor-corrector solution of the partial differential equation of atmospheric diffusion from a line source. The problem is solved in slices proceeding in a downwind direction,each slice requiring a matrix reduction. The equations of the system are the integrated conditions of Green taken over vertical strips of elements. The original equation is written so that the linearized terms carry the main burden,giving a predictor so accurate that little iteration is required. The report we introduce the idea of using two approximating nets when the demands of accuracy require a vertical step size too small for a stable process. One is a coarse net for the determination of the matrix,and values of the solution at points of the fine net are computed from Green's formula in an overdetermined fashion using boundary values coming from the coarse solution. In turn,the fine results can be used to improve the accuracy of the accuracy of the corrector for the coarse solution. (Author)