A robust numerical scheme for the simulation of nonlinear convection–diffusion–reaction equation

Abstract

In this article, the polynomial based differential quadrature method is used to develop a numerical scheme for solving convection–diffusion–reaction model with a general reaction term. The numerical scheme is found applicable to a wide set of problems including diffusion, convection–diffusion and diffusion–reaction. The validation of the method is performed through simulations of Newell-Whitehead, Burger-Fisher, and Burger-Huxley equations. The proposed numerical method is found better than many numerical methods presented in the literature. Vector form of numerical scheme is presented to implement algorithm efficiently. The compatibility, error and computational complexity of the numerical scheme are studied in detail.

Keywords:

• Newell-Whitehead equation
• Burger-Fisher equation
• Burgers-Huxley equation
• differential quadrature method
• quasilinearization technique

Acknowledgments

The authors are very grateful to Kerala State Council for Science, Technology and Environment (KSCSTE) for their financial support. We are thankful for the valuable comments and suggestions of the reviewers.