Given an orthogonal and uniform solution grid with equal spatial grid sizes, we construct a new second-order implicit conservative finite difference scheme for the fourth-order 2D Boussinesq paradigm equation with quadratic nonlinear part. We apply the algebraic approach to the construction of difference schemes suggested by the first two authors and based on a combination of the finite volume method, difference elimination, and numerical integration. For the difference elimination, we make use of the techniques of Gröbner bases; in so doing, we introduce an extra difference indeterminate to reduce the nonlinear elimination problem to the pure linear one. It allows us to apply the Gröbner bases algorithm and software designed for linear generating sets of difference polynomials. Additionally, for the obtained difference scheme and also for another scheme known in the literature, we compute the modified differential equations and compare them.

Authors

Language

English

Pages

152-163

Status

Published

Volume

11661 LNCS

Year

2019

Organizations

^{1}Saratov State University^{2}Joint Institute for Nuclear Research^{3}Peoples’ Friendship University of Russia^{4}Dubna State University

Keywords

Computer Algebra; conservativity; consistency; Difference elimination; finite difference approximation; Gröbner basis; Modified equation

Date of creation

20.02.2020

Date of change

20.02.2020

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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).
Vol. 11661 LNCS.
2019.
P. 140-151

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).
Vol. 11661 LNCS.
2019.
P. 91-106