Proper orthogonal decomposition Pascal polynomial-based method for solving Sobolev equation
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 17 November 2021
Issue publication date: 16 May 2022
Abstract
Purpose
This study aims to use the polynomial approximation method based on the Pascal polynomial basis for obtaining the numerical solutions of partial differential equations. Moreover, this method does not require establishing grids in the computational domain.
Design/methodology/approach
In this study, the authors present a meshfree method based on Pascal polynomial expansion for the numerical solution of the Sobolev equation. In general, Sobolev-type equations have several applications in physics and mechanical engineering.
Findings
The authors use the Crank-Nicolson scheme to discrete the time variable and the Pascal polynomial-based (PPB) method for discretizing the spatial variables. But it is clear that increasing the value of the final time or number of time steps, will bear a lot of costs during numerical simulations. An important purpose of this paper is to reduce the execution time for applying the PPB method. To reach this aim, the proper orthogonal decomposition technique has been combined with the PPB method.
Originality/value
The developed procedure is tested on various examples of one-dimensional, two-dimensional and three-dimensional versions of the governed equation on the rectangular and irregular domains to check its accuracy and validity.
Keywords
Acknowledgements
The authors thank the reviewers for their constructive comments and suggestions that improved the paper.
Citation
Dehghan, M., Hooshyarfarzin, B. and Abbaszadeh, M. (2022), "Proper orthogonal decomposition Pascal polynomial-based method for solving Sobolev equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 7, pp. 2506-2542. https://doi.org/10.1108/HFF-09-2021-0598
Publisher
:Emerald Publishing Limited
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