Numerical simulation of time fractional Kudryashov Sinelshchikov equation describing the pressure waves in a mixture of liquid and gas bubbles

Abstract

This article is concerned with an approximate analytical solution for the time fractional Kudryashov Sinelshchikov equation by using the reproducing kernel Hilbert space method. The main tools of this method are reproducing kernel theory, some important Hilbert spaces, the normal basis, orthogonalisation process, and homogenization. The effectiveness of reproduc ing kernel Hilbert space method is presented through the tables and graphs. These computa tional results indicate that this method is highly accurate and efficient for the time fractional Kudryashov Sinelshchikov equation. Also, it is demonstrated that the approximate solution uniformly converges to exact solution by using reproducing kernel Hilbert space method.