Cubic quasi-interpolation spline collocation method for solving convection–diffusion equations

In this paper, we use a cubic spline collocation method to solve a two dimensional convection–diffusion equation. More precisely, we approximate first and second order partial derivatives by those of cubic spline quasi-interpolants to produce a system of first order ordinary differential equations....

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Bibliographic Details
Published in:Mathematics and computers in simulation 2019-10, Vol.164, p.33-45
Main Authors: Bouhiri, S., Lamnii, A., Lamnii, M.
Format: Article
Language:English
Subjects:
B-spline
Collocation-method
Convection–diffusion equation
Quasi-interpolation
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Summary:In this paper, we use a cubic spline collocation method to solve a two dimensional convection–diffusion equation. More precisely, we approximate first and second order partial derivatives by those of cubic spline quasi-interpolants to produce a system of first order ordinary differential equations. The resulting system can be solved using MATLAB’s ode solver. Error estimates of quasi-interpolants which are used are given with full discussion. Furthermore, numerical examples are presented to show the validity of our methods.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2018.11.003