A quintic B-spline finite elements scheme for the KdVB equation

A quintic B-spline finite elements scheme for the KdVB equation An algorithm for solving the Korteweg de–vries Burgers' (KdVB) equation, based on the collocation method with quintic B-spline finite elements is set up to simulate the solutions of the KdV, Burgers' and the KdVB equations. The migration of solitary waves and temporal evolution of a Maxwellian initial pulse are studied for the KdV equation. Burgers' equation is solved for different values of Reynolds number. The time evaluation of the solutions of the KdVB equation with different values for the diffusion and dispersion coefficients is studied. Invariants and error norms are studied wherever possible to determine the conservation properties of the algorithm. A linear stability analysis shows the scheme to be unconditionally stable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computer Methods in Applied Mechanics and Engineering Elsevier

A quintic B-spline finite elements scheme for the KdVB equation

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Publisher
Elsevier
Copyright
Copyright © 2000 Elsevier Science S.A.
ISSN
0045-7825
eISSN
1879-2138
DOI
10.1016/S0045-7825(99)00142-5
Publisher site
See Article on Publisher Site

Abstract

An algorithm for solving the Korteweg de–vries Burgers' (KdVB) equation, based on the collocation method with quintic B-spline finite elements is set up to simulate the solutions of the KdV, Burgers' and the KdVB equations. The migration of solitary waves and temporal evolution of a Maxwellian initial pulse are studied for the KdV equation. Burgers' equation is solved for different values of Reynolds number. The time evaluation of the solutions of the KdVB equation with different values for the diffusion and dispersion coefficients is studied. Invariants and error norms are studied wherever possible to determine the conservation properties of the algorithm. A linear stability analysis shows the scheme to be unconditionally stable.

Journal

Computer Methods in Applied Mechanics and EngineeringElsevier

Published: Jul 21, 2000

References

  • Derivation of the Korteweg de–Vries and Burgers' equation
    Su, C.H.; Gardner, C.S.

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