Pointwise error estimates of the novel nonlinear fourth-order compact difference scheme for viscous Burgers’ equation

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Prof. Qifeng ZHANG
Associate Professor
Zhejiang Sci-Tech University


In this talk, a novel fourth-order three-point compact operator for the nonlinear convection term is provided. The operator makes the numerical analysis of higher order nonlinear or linearly implicit difference schemes become possible for a wide class of nonlinear evolutionary equations under the unified framework. We take the classical viscous Burgers’equation as an example and establish a new conservative fourth-order implicit compact difference scheme based on the method of order reduction. A detailed theoretical analysis is carried out. Furthermore, we derive a three-level linearized compact difference scheme for viscous Burgers’equation based on the proposed operator. Applying the compact operator to other more complex and higher-order nonlinear evolutionary equations is feasible, including Benjamin-Bona-Mahony-Burgers’equation, Korteweg-de Vries equation, Kuramoto-Sivashinsky equation, and classification to name a few. Numerical results confirm our results.


Prof. Qifeng ZHANG obtained his Ph.D. degree in Huazhong University of Science and Technology in 2014, works as an associate professor at Zhejiang Sci-Tech University. His main research interests include high-order numerical methods for delay PDEs and fractional PDEs, numerical solution for nonlinear evolutionary equations, preconditioning techniques and iterative methods for PDEs, etc. He has presided over one project of National Natural Science Foundation of China and two projects of Zhejiang Provincial Natural Science Foundation , published more than 20 papers on many international famous journals.

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