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  • 1
    Electronic Resource
    Electronic Resource
    A B-spline finite element method for the regularized long wave equation (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 59-68 
    Details
    ISSN: 1069-8299
    Keywords: RLW equation ; finite elements ; splines ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method with quadratic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution range. Time integration of the resulting system of ordinary differential equations is effected using a Crank-Nicolson approximation. Standard problems are used to validate the algorithm, which is then used to model the smooth development of an undular bore.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110109
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  • 2
    Electronic Resource
    Electronic Resource
    A least-squares finite element scheme for the RLW equation (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 795-804 
    Details
    ISSN: 1069-8299
    Keywords: RLW equation ; finite element methods ; Petrov-Galerkin ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The RLW equation is solved by a least-squares technique using linear space-time finite elements. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent difference scheme based on cubic spline interpolation functions. In addition, for very small amplitude waves (≤ 0.09) it has higher accuracy than an approach using quadratic B-spline finite elements within Galerkin's method. The development of an undular bore is modelled.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Simulations of the EW undular bore (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 583-592 
    Details
    ISSN: 1069-8299
    Keywords: RLW equation ; finite elements ; Petrov-Galerkin ; undular bore ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The equal width equation is solved by a Petrov-Galerkin method using quadratic B-spline spatial finite elements. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is obtained via a Crank-Nicolson approach involving a product approximation. The motion of solitary waves is studied to assess the properties of the algorithm. The development of an EW undular bore is investigated and compared with that of the RLW bore. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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