Affiliation:
1. ONDOKUZ MAYIS ÜNİVERSİTESİ, LİSANSÜSTÜ EĞİTİM ENSTİTÜSÜ, MATEMATİK (DR)
2. ONDOKUZ MAYIS ÜNİVERSİTESİ, EĞİTİM FAKÜLTESİ
Abstract
In this study, Banach contraction method (BCM), Daftardar-Jafari method (DJM) and modified variational iteration method (MVIM) are proposed for the semi-analytical solutions of the Kudryashov-Sinelshchikov (K-S) dynamical equation. It has been shown that the analytical and semi-analytical solutions for the K-S dynamical equation with initial value problems by using semi-analytical methods can be obtained. In addition, the effectiveness and usefulness of the semi-analytical methods used are supported by tables and 3D figures. As the number of iteration or terms increases, how the semi-analytical solutions behave over time and converge to the exact solution is shown in detail with 2D figures. Also, it is shown comparison of semi-analytical solutions with exact solutions and error analysis with the help of tables. It has been discussed the methods are compared with each other and whether they are suitable for the K-S dynamical equation.
Publisher
Turkish Journal of Mathematics and Computer Science, Association of Mathematicians
Reference33 articles.
1. Abassy, T.A., El Tawil, M., El Zoheiry, H., Toward a modified variational iteration method , Journal of Computational and Applied Mathematics, 207(2007), 137–147.
2. Abassy, T.A., Modified variational iteration method (nonlinear homogeneous initial value problem), Computers and Mathematics with Applications, 59(2010), 912–918.
3. Abbasbandy, S., Shivanian, E., Application of the variational iteration method for system of nonlinear Volterra’s integro-differential equations, Mathematical and Computational Applications, 14(2009), 147–158.
4. Abed, M.S., Al-Jawary, M.A.,Efficient iterative methods for solving the SIR epidemic model, Iraqi Journal of Science, 62(2021), 613–622.
5. Al-Jawary, M.A., Analytical solutions for solving fourth-order parabolic partial differential equations with variable coefficients, International Journal of Advances Scientific and Technical Research,3(2015), 531–545.