  A new implicit-explicit local differential transform method (IELDTM) is
derived here for time integration of the nonlinear advection-diffusion
processes represented by (2+1)-dimensional Burgers equation. The IELDTM is
adaptively constructed as stability preserved and high order time integrator
for spatially discretized Burgers equation. For spatial discretization of the
model equation, the Chebyshev spectral collocation method (ChCM) is utilized. A
robust stability analysis and global error analysis of the IELDTM are presented
with respect to the direction parameter \theta. With the help of the global
error analysis, adaptivity equations are derived to minimize the computational
costs of the algorithms. The produced method is shown to eliminate the accuracy
disadvantage of the classical \theta-method and the stability disadvantages of
the existing DTM-based methods. Two examples of the Burgers equation in one and
two dimensions have been solved via the ChCM-IELDTM hybridization, and the
produced results are compared with the literature. The present time integrator
has been proven to produce more accurate numerical results than the MATLAB
solvers, ode45 and ode15s.
