Tailored finite point method for solving one-dimensional Burgers’ equation. (English) Zbl 1364.65219
Summary: 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.
MSC:
65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
35Q35 | PDEs in connection with fluid mechanics |
35K55 | Nonlinear parabolic equations |
Keywords:
Burgers’ equation; Tailored finite point; Hopf-Cole transformation; viscous flows; explicit schemeReferences:
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.