A new conservative finite difference scheme for Boussinesq paradigm equation

Natalia Kolkovska; Milena Dimova

Open Mathematics (2012)

  • Volume: 10, Issue: 3, page 1159-1171
  • ISSN: 2391-5455

Abstract

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A family of nonlinear conservative finite difference schemes for the multidimensional Boussinesq Paradigm Equation is considered. A second order of convergence and a preservation of the discrete energy for this approach are proved. Existence and boundedness of the discrete solution on an appropriate time interval are established. The schemes have been numerically tested on the models of the propagation of a soliton and the interaction of two solitons. The numerical experiments demonstrate that the proposed family of schemes is about two times more accurate than the family of schemes studied in [Kolkovska N., Two families of finite difference schemes for multidimensional Boussinesq paradigm equation, In: Application of Mathematics in Technical and Natural Sciences, Sozopol, June 21–26, 2010, AIP Conf. Proc., 1301, American Institute of Physics, Melville, 2010, 395–403].

How to cite

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Natalia Kolkovska, and Milena Dimova. "A new conservative finite difference scheme for Boussinesq paradigm equation." Open Mathematics 10.3 (2012): 1159-1171. <http://eudml.org/doc/269543>.

@article{NataliaKolkovska2012,
abstract = {A family of nonlinear conservative finite difference schemes for the multidimensional Boussinesq Paradigm Equation is considered. A second order of convergence and a preservation of the discrete energy for this approach are proved. Existence and boundedness of the discrete solution on an appropriate time interval are established. The schemes have been numerically tested on the models of the propagation of a soliton and the interaction of two solitons. The numerical experiments demonstrate that the proposed family of schemes is about two times more accurate than the family of schemes studied in [Kolkovska N., Two families of finite difference schemes for multidimensional Boussinesq paradigm equation, In: Application of Mathematics in Technical and Natural Sciences, Sozopol, June 21–26, 2010, AIP Conf. Proc., 1301, American Institute of Physics, Melville, 2010, 395–403].},
author = {Natalia Kolkovska, Milena Dimova},
journal = {Open Mathematics},
keywords = {Conservative finite difference scheme; Boussinesq Paradigm Equation; Solitary waves; solitary waves; nonlinear conservative finite difference schemes; multidimensional Boussinesq paradigm equation; convergence; numerical experiments; soliton},
language = {eng},
number = {3},
pages = {1159-1171},
title = {A new conservative finite difference scheme for Boussinesq paradigm equation},
url = {http://eudml.org/doc/269543},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Natalia Kolkovska
AU - Milena Dimova
TI - A new conservative finite difference scheme for Boussinesq paradigm equation
JO - Open Mathematics
PY - 2012
VL - 10
IS - 3
SP - 1159
EP - 1171
AB - A family of nonlinear conservative finite difference schemes for the multidimensional Boussinesq Paradigm Equation is considered. A second order of convergence and a preservation of the discrete energy for this approach are proved. Existence and boundedness of the discrete solution on an appropriate time interval are established. The schemes have been numerically tested on the models of the propagation of a soliton and the interaction of two solitons. The numerical experiments demonstrate that the proposed family of schemes is about two times more accurate than the family of schemes studied in [Kolkovska N., Two families of finite difference schemes for multidimensional Boussinesq paradigm equation, In: Application of Mathematics in Technical and Natural Sciences, Sozopol, June 21–26, 2010, AIP Conf. Proc., 1301, American Institute of Physics, Melville, 2010, 395–403].
LA - eng
KW - Conservative finite difference scheme; Boussinesq Paradigm Equation; Solitary waves; solitary waves; nonlinear conservative finite difference schemes; multidimensional Boussinesq paradigm equation; convergence; numerical experiments; soliton
UR - http://eudml.org/doc/269543
ER -

References

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