# 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

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topNatalia 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 -

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