A stability preserved time-integration method for nonlinear advection–diffusion-reaction processes

A new implicit-explicit local differential transform method (IELDTM) is derived here for time integration of the nonlinear (2 + 1)-dimensional advection–diffusion-reaction (ADR) equations. The IELDTM adaptively constructed as a stability preserved and high order integrator spatially discretized ADR For spatial discretization model equation, Chebyshev spectral collocation (ChCM) utilized. robust analysis global error are presented with respect to direction parameter $$\theta $$ . With help analysis, adaptivity equations minimize computational costs algorithms. produced shown eliminate accuracy disadvantage classical -method disadvantages existing transform-based methods. Two examples Burgers equation in one two space dimensions Chapman oxygen-ozone solved via ChCM-IELDTM hybridization. present proven provide more efficient numerical characteristics than various multi-step multi-stage extensively compared widely used MATLAB solvers, ode45 ode15s. adaptive has been integrate stiff optimum over relatively long-time intervals.