Abstract
A multi-domain Galerkin method is presented for the Burgers equation, whose solutions behave differently at positive infinity and negative infinity. The original problem is transformed into a problem with general variable coefficients and homogeneous boundary conditions at infinities by using the auxiliary function, which is capable of being reformulated as a suitable variational formulation that is the most convenient for analysing numerical error. As an application, the composite spectral scheme with numerical integration is provided for the underlying problem on the whole line, which is easy to deal with problems concerning general variable coefficients. Some composite generalized Laguerre–Legendre interpolations on the whole line are established. The convergence and stability of the proposed algorithm are proved. Numerical results show the efficiency of this approach and agree well with the theoretical analysis.
Acknowledgments
The authors would like to thank the anonymous referees, Dr Yue Zhu of Hangzhou Dianzi University, Dr Lu-yu Wang of Zhejiang University and Jun-jie Zheng of East China University of Political Science and Law for their help on polishing this work.
Disclosure statement
The author confirm that this article has no competing interests with any institution or individual.