Local Discontinuous Galerkin Method for Solving Compound Nonlinear KdV-Burgers Equations

In this work, an efficient local discontinuous Galerkin scheme is applied to numerically solve the nonlinear compound KdV-Burgers equation. The numerical scheme utilizes a local discontinuous Galerkin discretization technique in the spatial direction coupled with a higher order strong-stability-preserving Runge-Kutta scheme in the temporal direction. The L-2 stability analysis of the implemented numerical scheme, along with a detailed error estimate for smooth solutions, are also established by carefully selecting the interface numerical fluxes. In addition, numerical simulations are carried out using several illustrative examples, and the results obtained are then compared with solutions acquired by the analytical exp(-Phi(xi))-expansion method to validate the acceptable accuracy and plausibility of the proposed numerical technique. Also, both two-dimensional and three-dimensional graphical representations are presented to visually demonstrate the physical significance of the resulting traveling wave solutions.