Numerical simulation of the generalized modified Benjamin–Bona–Mahony equation using SBP-SAT in time

In this paper we present high-order accurate finite difference approximations for solving the generalized modified Benjamin–Bona–Mahony (BBM) equation, a non-linear soliton model. The spatial discretization uses high-order accurate summation-by-parts (SBP) finite difference operators combined with b...

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Vydáno v:	Journal of computational and applied mathematics Ročník 459; s. 116377
Hlavní autoři:	Kjelldahl, Vilma, Mattsson, Ken
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier B.V 15.05.2025
Témata:	Benjamin-Bona-Mahony equation Beräkningsvetenskap med inriktning mot numerisk analys Boundary conditions Initial boundary value problem Non-linear Scientific Computing with specialization in Numerical Analysis Simultaneous-approximation-terms Summation-by-parts Time integration Initial boundary value problem Benjamin–Bona–Mahony equation Summation-by-parts Non-linear Boundary conditions Time integration Simultaneous-approximation-terms
ISSN:	0377-0427, 1879-1778
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Abstract	In this paper we present high-order accurate finite difference approximations for solving the generalized modified Benjamin–Bona–Mahony (BBM) equation, a non-linear soliton model. The spatial discretization uses high-order accurate summation-by-parts (SBP) finite difference operators combined with both weak and strong enforcement of boundary conditions. For time integration we compare the explicit RK4 method against an implicit SBP time integrator. These time-marching methods are evaluated and compared in terms of accuracy and efficiency. It is shown that the implicit SBP time-integrator is more efficient than the explicit RK4 method for non-linear soliton models. •Stable approximations of the generalized modified BBM equation are derived.•An implicit SBP-SAT temporal discretization is derived.•The SBP-SAT temporal discretization, as compared to RK4, is much more efficient.•SBP-Projection is a more favourable method of imposing BC, as compared to SAT.
AbstractList	In this paper we present high-order accurate finite difference approximations for solving the generalized modified Benjamin–Bona–Mahony (BBM) equation, a non-linear soliton model. The spatial discretization uses high-order accurate summation-by-parts (SBP) finite difference operators combined with both weak and strong enforcement of boundary conditions. For time integration we compare the explicit RK4 method against an implicit SBP time integrator. These time-marching methods are evaluated and compared in terms of accuracy and efficiency. It is shown that the implicit SBP time-integrator is more efficient than the explicit RK4 method for non-linear soliton models. •Stable approximations of the generalized modified BBM equation are derived.•An implicit SBP-SAT temporal discretization is derived.•The SBP-SAT temporal discretization, as compared to RK4, is much more efficient.•SBP-Projection is a more favourable method of imposing BC, as compared to SAT. In this paper we present high-order accurate finite difference approximations for solving the generalized modified Benjamin-Bona-Mahony (BBM) equation, a non-linear soliton model. The spatial discretization uses high-order accurate summation-by-parts (SBP) finite difference operators combined with both weak and strong enforcement of boundary conditions. For time integration we compare the explicit RK4 method against an implicit SBP time integrator. These time-marching methods are evaluated and compared in terms of accuracy and efficiency. It is shown that the implicit SBP time-integrator is more efficient than the explicit RK4 method for non-linear soliton models.
ArticleNumber	116377
Author	Kjelldahl, Vilma Mattsson, Ken
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Cites_doi	10.1016/j.joes.2017.08.006 10.1016/j.jcp.2013.05.042 10.1016/j.jcp.2018.06.030 10.1006/jcph.1994.1057 10.1016/j.jcp.2014.06.027 10.1006/jcph.1994.1005 10.1016/S0168-9274(02)00138-1 10.1016/j.jcp.2022.111743 10.1016/j.physleta.2006.03.005 10.1016/j.jcp.2014.03.048 10.1090/S0025-5718-1995-1308459-9 10.1016/j.heliyon.2022.e12122 10.1016/j.jcp.2019.07.018 10.1137/15M1014917 10.1016/j.jcp.2004.03.001 10.1090/S0025-5718-1995-1297474-X 10.1007/BF01386051 10.1007/BF01939406
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Keywords	Initial boundary value problem Benjamin–Bona–Mahony equation Summation-by-parts Non-linear Boundary conditions Time integration Simultaneous-approximation-terms
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SubjectTerms	Benjamin-Bona-Mahony equation Beräkningsvetenskap med inriktning mot numerisk analys Boundary conditions Initial boundary value problem Non-linear Scientific Computing with specialization in Numerical Analysis Simultaneous-approximation-terms Summation-by-parts Time integration
Title	Numerical simulation of the generalized modified Benjamin–Bona–Mahony equation using SBP-SAT in time
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