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ABSTRACT
We propose a tailored finite point method (TFPM) for solving a quasilinear time-dependent Burgers' equation with a small coefficient of viscosity. The selected basis functions for the TFPM automatically fit the properties of the local solution in time and space simultaneously. The stability and error analysis for the TFPM are given. We also demonstrate the efficiency of the proposed scheme on relatively coarse meshes. The numerical results indicate that the TFPM achieves high accuracy and effectively captures the shock solutions.
Acknowledgments
The authors would like to thank the anonymous referees for their kind comments and valuable suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
This work was supported by the Ministry of Science and Technology of Taiwan through Project MOST 103-2115-M-005-004-MY2 and MOST 103-2811-M-005-032.