This study reports novel hybrid computational methods for the solutions of nonlinear singular Lane-Emden type differential equation arising in astrophysics models by exploiting the strength of unsupervised neural network models and stochastic optimization techniques. In the scheme the neural network, sub-part of large field called soft computing, is exploited for modelling of the equation in an...

nonlinear difference equations of higher order are important in applications; such equations appear naturally as discrete analogues of differential and delay differential equations which model various diverse phenomena in biology, ecology, economics, physics and engineering. the study of dynamical properties of such equations is of great importance in many areas. the autonomous difference equat...

in this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of tvd (total variation diminishing) of the solution, is proposed. this scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. schemes preserving the essential physical property of tvd are of great importance in practice. such s...

Persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrödinger (NLS) equation is addressed. The discrete NLS equation with the most general cubic polynomial function is considered. Constraints on the nonlinear function are found from the condition that the second-order difference equation for stationary solutions can be redu...

In this paper, a rational difference equation with positive parameters and non-negative conditions is used to determine the presence direction of Neimark–Sacker bifurcation. The neimark–Sacker bifurcation system first studied using characteristic equation. addition, we study invariant curves from perspective normal form theory. A computer simulation illustrate analytical results.