New analytical solutions for the Oskolkov-type equations in fluid dynamics via a modified methodology

Abstract

The main goal of this paper is to propose an efficient technique in solving partial differential equations inspired by the improvement of a known method. To this end, we modified the generalized exponential rational function method to obtain analytical solutions for two Oskolkov-type equations. The basic idea of this improvement will be to consider a new formality structure for the desired solution to the problem. The basic premise for solutions is an effective combination of exponential functions in fractional form. Numerical simulations obtained by the proposed method have been also included. The results confirm that the technique is effective and straightforward. After making some necessary changes, the introduced technique can be used to solve many other nonlinear problems. Due to the high volume of symbolic calculations while solving the equation, it is necessary to employ a symbolic computing package in known mathematical softwares such as Mathematica or Maple.

Keywords

• Efficient methods
• The Oskolkov-type equations
• Analytic wave solutions
• Symbolic computations