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    A novel perspective for simulations of the MEW equation by trigonometric cubic B-spline collocation method based on Rubin-Graves type linearization
    (Univ Tabriz, 2022) Yagmurlu, Nuri Murat; Karakas, Ali Sercan
    In the present study, the Modified Equal Width (MEW) wave equation is going to be solved numerically by presenting a new technique based on the collocation finite element method in which trigonometric cubic B-splines are used as approximate functions. In order to support the present study, three test problems; namely, the motion of a single solitary wave, the interaction of two solitary waves, and the birth of solitons are studied. The newly obtained results are compared with some of the other published numerical solutions available in the literature. The accuracy of the proposed method is discussed by computing the numerical conserved laws as well as the error norms L2 and Loo.
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    A novel perspective for simulations of the Modified Equal-Width Wave equation by cubic Hermite B-spline collocation method
    (Elsevier, 2024) Kutluay, Selcuk; Yagmurlu, Nuri Murat; Karakas, Ali Sercan
    In the current study, the Modified Equal -Width (MEW) equation will be handled numerically by a novel technique using collocation finite element method where cubic Hermite B -splines are used as trial functions. To test the accuracy and efficiency of the method, four different experimental problems; namely, the motion of a single solitary wave, interaction of two solitary waves, interaction of three solitary waves and the birth of solitons with the Maxwellian initial condition will be investigated. In order to verify, the validity and reliability of the proposed method, the newly obtained error norms L 2 and L infinity as well as three conservation constants have been compared with some of the other numerical results given in the literature at the same parameters. Furthermore, some wave profiles of the newly obtained numerical results have been given to demonstrate that each test problem exhibits accurate physical simulations. The advantage of the proposed method over other methods is the usage of inner points at Legendre and Chebyshev polynomial roots. This advantage results in better accuracy with less number of elements in spatial direction. The results of the numerical experiments clearly reveal that the presented scheme produces more accurate results even with comparatively coarser grids.
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    Numerical solutions of the equal width equation by trigonometric cubic B-spline collocation method based on Rubin-Graves type linearization
    (Wiley, 2020) Yagmurlu, Nuri Murat; Karakas, Ali Sercan
    In this article, the equal width (EW) equation is going to be solved numerically. In order to show the accuracy of the presented method, six test problems namely single solitary wave, interaction of two solitary waves, interaction of three solitary waves, Maxwellian initial condition, undular bore, and soliton collision are going to be solved. For the first test problem, since it has exact solution, the error norms L-2 and L-infinity are going to be calculated and compared with some of the earlier studies existing in the literature. Moreover, the three invariants I-1, I-2, and I-3 of the given problems during the simulations are calculated and tabulated. Besides those comparisons, the relative changes of the invariants are given. Finally, a comparison of those error norms and invariants has clearly shown that the present approach obtained compatible and better results than most of the earlier works by using the same parameters.