Discontinuous Legendre wavelet Galerkin method for reaction–diffusion equation

ABSTRACT

This paper proposes a novel numerical method, that is, discontinuous Legendre wavelet Galerkin technique for solving reaction–diffusion equation (RDE). Specifically, variational formulation and corresponding numerical fluxes of this type equation are devised by utilizing the advantages of both Legendre wavelet bases and discontinuous Galerkin approach. Furthermore, adaptive algorithm, stability and error analysis of this method have been discussed. Especially, the distinctive features of the presented approach are easy to cope with a variety of boundary conditions and able to effectively approximate solution of the RDE with less execution and storage space. Finally, numerical tests affirm better accuracy for a range of benchmark problems and demonstrate the validity and utility of this approach.

KEYWORDS:

• Legendre wavelet
• discontinuous Galerkin method
• Legendre wavelet Galerkin method
• discontinuous Legendre wavelet Galerkin method
• reaction–diffusion equation

2010 AMS SUBJECT CLASSIFICATIONS:

• 65D99
• 65N99
• 41A25
• 44A45

Acknowledgements

The authors are grateful to the editor and referees for their valuable comments that greatly improve the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is funded by Fundamental and Advanced Research Project of Chongqing CSTC of China, the project No. are CSTC2013JCYJA00022 and cstc2012jjA00018 and is supported by Technological Research Program of Chongqing Municipal Education Commission [Grant No.KJ130810 and KJ1400937].