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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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 459; p. 116377
Main Authors: Kjelldahl, Vilma, Mattsson, Ken
Format: Journal Article
Language:English
Published: Elsevier B.V 15.05.2025
Subjects:
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
Online Access:Get full text
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2024.116377