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Author: Aydin, A.Scopus Q: Q4

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    Citation - WoS: 6
    An Unconventional Splitting for Korteweg de Vries-Burgers Equation
    (European Journal Pure & Applied Mathematics, 2015) Aydin, A.
    Numerical solutions of the Korteweg de Vries-Burgers (KdVB) equation based on splitting is studied. We put a real parameter into a KdVB equation and split the equation into two parts. The real parameter that is inserted into the KdVB equation enables us to play with the splitted parts. The real parameter enables to write the each splitted equation as close to the Korteweg de Vries (KdV) equation as we wish and as far from the Burgers equation as we wish or vice a versa. Then we solve the splitted parts numerically and compose the solutions to obtained the integrator for the KdVB equation. Finally we present some numerical experiments for the solution of the KdV, Burger's and KdVB equations. The numerical experiments shows that the new splitting gives feasible and valid results.
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    Conference Object
    Citation - WoS: 1
    Operator Splitting of the Kdv-Burgers Type Equation With Fast and Slow Dynamics
    (Amer inst Physics, 2010) Aydin, A.; Karasozen, B.
    The Korteweg de Vries-Burgers (KdV-Burgers) type equation arising from the discretization of the viscous Burgers equation with fast dispersion and slow diffusion is solved using operator splitting. The dispersive and diffusive parts are discretized in space by second order conservative finite differences. The resulting system of ordinary differential equations are composed using the time reversible Strang splitting. The numerical results reveal that the periodicity of the solutions and the invariants of the KdV-Burgers equation are well preserved.
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    Conference Object
    Citation - WoS: 1
    Multisymplectic Schemes for the Complex Modified Korteweg-De Vries Equation
    (Amer inst Physics, 2008) Aydin, A.; Karasoezen, B.
    In this paper, the multisymplectic formulation of the CMKdV(complex modified Korteweg-de Vries equation) is derived. Based on the multisymplectic formulation, the eight-point multisymplectic Preissman scheme and a linear-nonlinear multisymplectic splitting scheme are developed. Both methods are compared numerically with respect to the conservation of local and global quantities of the CMKdV equation.