We present a nonlinear partial difference equation defined on a square which is obtained by combining the Miura transformations between the Volterra and the modified Volterra differential-difference equations. This equation is not symmetric with respect to the exchange of the two discrete variables and does not satisfy the 3D-consistency condition necessary to belong to the Adler-Bobenko-Suris ...

The purpose of this paper is concerned with the mathematical model development issues, necessary for a better prediction of dynamic responses of articulated rotor helicopters. The methodology is laid out based on mathematical model development for an articulated rotor helicopters, using the theories of aeroelastisity, finite element and the time domain compressible unsteady aerodynamics. The he...

this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

Motivated by ongoing work in the theory of stochastic partial differential equations we develop direct methods to infer that the Galerkin approximations of certain nonlinear partial differential equations are Cauchy (and therefore convergent). We develop such a result for the Navier–Stokes equations in space dimensions two and three, and for the primitive equations in space dimension two. The a...

The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. The governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (NODE) by using a classical similarity transformation along with appropriate boundary cond...

MHD boundary layer flow of two phase model nanofluid over a vertical plate is investigated both analytically and numerically. A system of governing nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations by suitable similarity transformations and then solved analytically using homotopy analysis method and numerically by the fourth order Rung...

We use the improved general mapping deformationmethod based on the generalized Jacobi elliptic functions expansionmethod to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical physics via the generalized nonlinear Klein-Gordon equation and the classical Boussinesq equations. As a result, some new generalized Jacobi ellipt...

Taking the example of Koretweg–de Vries equation, it is shown that soliton solutions need not always be the consequence of the trade-off between the nonlinear terms and the dispersive term in the nonlinear differential equation. Even the ordinary one dimensional linear partial differential equation can produce a soliton. Solitary waves and solitons are often described [1-8] as a consequence of ...

Purpose – The purpose of this paper is to use the polynomial differential quadrature method (PDQM) to find the numerical solutions of some Burgers’-type nonlinear partial differential equations. Design/methodology/approach – The PDQM changed the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs). The obtained system of ODEs is solved by Ru...

In the paper, we extend the differential transform method to solve nonlinear fractional partial differential equations. The timeand space-fractional Burgers equations with initial conditions are chosen to illustrate our method. As a result, we successfully obtain some available approximate solutions of them. The results reveal that the proposed method is very effective and simple for obtaining ...