The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches applied. However, nonlinear partial (PDEs) pose substantial challenges from inferential perspective, most notably the absence explicit conditioning formula. This paper extends earlier work on linear PDEs a general class initial value problems specified by PDEs, motiv...

Nonlinear partial diferential equations are a class of partial diferential equations having many important uses in engineering and sciences. In this work we display a comparison between Adomian Decomposition Method (ADM) and Differential Quadrature Method (DQM) for solving some nonlinear partial diferential equations. We found the existence of exact solutions for those models. The numerical res...

in this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation.this method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation and c...

We study the existence theory to quasistatic initial-boundary value problems with internal variables, which model the viscoelastic or viscoplastic behavior of solids at small strain. In these problems a system of linear partial differential equations coupled with a nonlinear system of differential equations or differential inclusions must be solved. The solution theory is based on monotonicity ...

Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudostable and pseudo-unstable manifolds for a class of random partial differential equations and stochastic partial differential equations is shown. Unlike the invarian...

In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical and engineering problems linear and nonlinear. In this article, we shall use the homotopy perturbation method (HPM) to solve some systems of partial differential equations viz. the systems of coupled Burgers’ equations in oneand twodimensions and the system of Laplace’s equation. This a...

Symmetries play an important role in solving partial differential equations. In this paper, the determining equations for a class of nonlinear partial differential equations with arbitrary order are considered. It is shown that the determining equations for the nonclassical reduction can be obtained by requiring the compatibility between the original equation and the invariant surface condition...

in the present paper, the flow and heat transfer of two types of nanofluids, namely, silver-water and silicon dioxide-water, were theoretically analyzed over an isothermal continues stretching sheet. to this purpose, the governing partial differential equations were converted to a set of nonlinear differential equations using similarity transforms and were then analytically solved. it was found...

In the presented paper, the governing equations of a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. The beam is homogenous, isotropic and it is subjected to the dynamic transverse and axial loads. The kinematic of the problem is according to the Von-Karman strain-displacement relations and the Hook's law is used as the constitutive eq...

Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differential-difference equations are presented. The first algorithm is the well-known Painlevé test, which is applicable to polynomial systems of ordinary and partial differential equations. The second and third algorithms allow one to explicitly compute polynomial conserved densities and ...