Efficient Solutions for Nonlinear Diffusion Equations Appeared as Models of Physical Problems

Abstract

The differential transform technique (DTM) looks promise for dealing with functional problems. Recent articles have demonstrated the DTM's efficiency in tackling a wide range of issues in many disciplines. In this paper, (DTM) is used to develop approximate, and exact solutions for some nonlinear diffusion equations. Nonlinear diffusion equations are used to describe processes and behaviours in fields of biology, heat transfer, chemical reactions, and mathematical physics. The differential transform method linked with Laplace transform and Pad’e approximation is used to improve some known results. The obtained solutions are compared with the exact known solutions, showing excellent agreement. The differential transformation method was used in conjunction with the use of the Laplace transform and the Pad’e approximation method, for the purpose of improving some calculations in the hope of obtaining a more accurate solution. The results were presented in the form of tables or graphics for the purpose of comparing the calculated solution and comparing it with some of the precise solutions presented previously. The results showed the accuracy of the agreement between the two solutions. This gives us the opportunity to use the method under consideration to find solutions to unknown problems and thus ensure the credibility of the calculated solution.