Abstract:
The two dimensional coupled Burgers' equations constitute an appropriate
model for developing computational algorithms, for solving the incompress-
ible Navier-Stokes equations. Moreover, they are generally used as transport
equations because they model a number of
uid
ow phenomena, for example,
turbulent
ow, shock wave formation and boundary layer formation. In this
paper, we develop a hybrid Crank-Nicolson and Du Fort and Frankel (CN-
DF) scheme. The hybrid CN-DF is developed by introducing the Du Fort and
Frankel (DF) properties into the Crank-Nicolson scheme (CN). This is a three-
level scheme and is also unconditionally stable. Numerical solutions from the
hybrid scheme are obtained by the use of MATLAB software. By use of L1
error, it is determined that the hybrid scheme is fth order accurate in space
and produces better results in comparison to the pure Crank-Nicolson and the
pure Du Fort and Frankel schemes.
