On Universality of Transition to Chaos Scenario in Nonlinear Systems of Ordinary Differential Equations of Shilnikov’s Type

Differential transform method for a a nonlinear system of differential equations arising in HIV infection of CD4+T cell

In this paper, differential transform method (DTM) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in HIV infections of cell. Intervals of validity of the solution will be extended by using Pade approximation. The results also will be compared with those results obtained by Runge-Kutta method. The technique is described and is illustrat...

Solving nonlinear Lane-Emden type equations with unsupervised combined artificial neural networks

In this paper we propose a method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-innite domain. The proposed approach is based on an Unsupervised Combined Articial Neural Networks (UCANN) method. Firstly, The trial solutions of the differential equations are written in the form of feed-forward neural networks cont...

Free Convection Flow and Heat Transfer of Nanofluids of Different Shapes of Nano-Sized Particles over a Vertical Plate at Low and High Prandtl Numbers

In this paper, free convection flow and heat transfer of nanofluids of differently-shaped nano-sized particles over a vertical plate at very low and high Prandtl numbers are analyzed.  The governing systems of nonlinear partial differential equations of the flow and heat transfer processes are converted to systems of nonlinear ordinary differential equation through similarity transformations. T...

Universality of Transition to Chaos in All Kinds of Nonlinear Differential Equations

Insight into the Boundary Layer Flows of Free Convection and Heat Transfer of Nanofluids over a Vertical Plate using Multi-Step Differential Transformation Method

This paper presents an insight into the boundary layer of free convection and heat transfer of nanofluids over a vertical plate at very low and high Prandtl number. Suitable similarity variables are used to convert the governing systems of nonlinear partial differential equations of the flow and heat transfer to systems of nonlinear ordinary differential equations which are solved using multi-s...