期刊
APPLIED MATHEMATICAL MODELLING
卷 40, 期 7-8, 页码 4586-4611出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2015.11.041
关键词
Advection-diffusion equation; Cubic trigonometric B-spline basis functions; Cubic trigonometric B-spline collocation method; Interpolation function; Thomas algorithm
资金
- FRGS from the School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia [203/PMATHS/6711324]
A new cubic trigonometric B-spline collocation approach is developed for the numerical solution of the advection-diffusion equation with Dirichlet and Neumann's type boundary conditions. The approach is based on the usual finite difference scheme to discretize the time derivative while a cubic trigonometric B-spline is utilized as an interpolation function in the space dimension with the help of theta-weighted scheme. The present scheme stabilizes the oscillations that are normally displayed by the approximate solution of the transient advective-diffusive equation in the locality of sharp gradients produced by transient loads and boundary layers. The scheme is shown to be stable and the accuracy of the scheme is tested by application to various test problems. The proposed approach is numerically verified to second order and shown to work for the Peclet number <= 5. (C) 2015 Elsevier Inc. All rights reserved.
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