BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-83-01
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: Stability analysis of finite difference schemes for the
               advection-diffusion equation
        TYPE:: Manuscript
      AUTHOR:: Chan, Tony F.
        DATE:: January 1983
       PAGES:: 24
    ABSTRACT:: We present a collection of stability results for finite
               difference approximations to the advection-diffusion equation
               $u_t\ = a u_x\ + b u_{xx}$. The results are for centered
               difference schemes in space and include explicit and implicit
               schemes in time up to fourth order and schemes that use
               different space and time discretizations for the advective
               and diffusive terms. The results are derived from a uniform
               framework based on the Schur-Cohn theory of Simple von
               Neumann Polynomials and are necessary and sufficient for the
               stability of the Cauchy problem. Some of the results are
               believed to be new.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-83-01