Tailored finite point method for solving one-dimensional Burgers' equation. Issue 4 (3rd April 2017) - Tsai, Chih-Ching; Shih, Yin-Tzer; Lin, Yu-Tuan; Wang, Hui-Ching
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.