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A new implicit-explicit local differential transform method (IELDTM) isderived here for time integration of the nonlinear advection-diffusionprocesses represented by (2+1)-dimensional Burgers equation. The IELDTM isadaptively constructed as stability preserved and high order time integratorfor spatially discretized Burgers equation. For spatial discretization of themodel equation, the Chebyshev spectral collocation method (ChCM) is utilized. Arobust stability analysis and global error analysis of the IELDTM are presentedwith respect to the direction parameter \theta. With the help of the globalerror analysis, adaptivity equations are derived to minimize the computationalcosts of the algorithms. The produced method is shown to eliminate the accuracydisadvantage of the classical \theta-method and the stability disadvantages ofthe existing DTM-based methods. Two examples of the Burgers equation in one andtwo dimensions have been solved via the ChCM-IELDTM hybridization, and theproduced results are compared with the literature. The present time integratorhas been proven to produce more accurate numerical results than the MATLABsolvers, ode45 and ode15s.

A stability preserved time-integration method for nonlinear advection-diffusion models