DISTRIBUTED APPROXIMATING FUNCTIONAL-APPROACH TO BURGERS-EQUATION IN ONE AND 2 SPACE DIMENSIONS

The method of distributed approximating functionals (DAFs) is applied to Burgers' equation, as a typical nonlinear PDE, in one and two space dimensions. This equation is similar to, but simpler than, the Navier -Stokes equation in fluid dynamics. The present approach uses DAFs for spatial discretization and a Taylor expansion for time discretization . Several moderately large values of the Reynolds number are considere d in the present application. The results obtained, which are in excel lent agreement with the formally exact series solutions, are compared with those obtained by other authors using various different methods, It is found that a simple numerical propagation scheme based on DAFs p rovides highly accurate numerical solutions for Burgers' equation, whi le requiring very few grid points, (C) 1998 Elsevier Science B.V.