In this paper, the piecewise parabolic method is presented for solving one-dimensional advection-diffusion type equation and its application to burger equation. First, given solution domain discretized by using a uniform Discretization grid point. Next applying integration in terms of spatial variable, we converting it into system first-order ordinary differential temporarily variable. Next, Ta...

We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de VriesHuxley, and Korteveg-de Vries-Burgers-Huxley equations, which combine effects of diffusion, dispersion, and nonlinearity. We emphasize the chiral behavior of the travelling solutions, whose velocities are determined by the p...

In this paper, a numerical scheme for solution of Generalized Burgers-Huxley equation using improved Nodal integral method (MNIM) is proposed. In this approach, the domain is divided into nodes and the derivation of the scheme is based on local transverse integration process (TIP) of PDEs within these nodes. A set of algebraic equations, based on the local analytical solution of ODEs obtained b...

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

The Time Fractional Burger equation was solved in this study using the Mabel software and Variational Iteration approach. where a number of instances Equation were handled technique. Tables images used to present collected numerical results. difference between exact solutions demonstrates effectiveness program’s solution, as well accuracy closeness results method produced. It also ability quick...

A phase-reduced model for weakly coupled Hodgkin-Huxley neurons, in particular its thermodynamic limit – the McKean-Vlasov equation is considered. Synaptic interactions require that phase interaction function consists of at least two competing Fourier modes representing an attractive and a repulsive contribution. The stationary permits finite-dimensional reduction terms generalized modified Bes...

some necessary and sufficient conditions are given for the existence of a g-positive (g-repositive) solution to adjointable operator equations $ax=c,axa^{left( astright) }=c$ and $axb=c$ over hilbert $c^{ast}$-modules, respectively. moreover, the expressions of these general g-positive (g-repositive) solutions are also derived. some of the findings of this paper extend some known results in the...

This article presents a flatness–based approach to the trajectory planning and feedforward control problem for the inviscid Burger equation with and without an additional quadratic nonlinearity. It uses the property of formal power series parameterizability of the underlying partial differential equation and uniform Euler–summability of the resulting power series to derive a parameterization of...