Distributed approximating functional approach to Burgersʹ equation in one and two space dimensions Original Research Article

The method of distributed approximating functionals (DAFs) is applied to Burgersʹ 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 considered in the present application. The results obtained, which are in excellent 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 provides highly accurate numerical solutions for Burgersʹ equation, while requiring very few grid points.