On the Semi-Analytical Solutions for the Kudryashov-Sinelshchikov Dynamical Equation Arising in Mixtures of Liquid and Gas Bubbles without Neglecting of Heat Transfer and Viscosity

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. © MatDer.