Browsing by Author "Koroglu, Canan"

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    Citation - WoS: 8
    Citation - Scopus: 9
    A nonstandard numerical method for the modified KdV equation
    (indian Acad Sciences, 2017) Aydin, Ayhan; Koroglu, Canan; Mathematics
    A linearly implicit nonstandard finite difference method is presented for the numerical solution of modified Korteweg-de Vries equation. Local truncation error of the scheme is discussed. Numerical examples are presented to test the efficiency and accuracy of the scheme.
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    Citation - WoS: 4
    Citation - Scopus: 5
    An Unconventional Finite Difference Scheme for Modified Korteweg-De Vries Equation
    (Hindawi Ltd, 2017) Koroglu, Canan; Aydin, Ayhan; Mathematics
    A numerical solution of the modified Korteweg-de Vries (MKdV) equation is presented by using a nonstandard finite difference (NSFD) scheme with theta method which includes the implicit Euler and a Crank-Nicolson type discretization. Local truncation error of the NSFD scheme and linear stability analysis are discussed. To test the accuracy and efficiency of the method, some numerical examples are given. The numerical results of NSFD scheme are compared with the exact solution and a standard finite difference scheme. The numerical results illustrate that the NSFD scheme is a robust numerical tool for the numerical integration of the MKdV equation.