and Applied Analysis 3 hard to obtain because they are highly nonlinear equations and most probably they are not integrable equations in general. Thus, large numbers of research results are still concentrated in the classical KdV equation and some other high-order equations with KdV type, such as KdV-Burgers equation [17, 18] and KdV-Burgers-Kuramoto equation [19], at present. Therefore, the in...

In this paper, three dimensional (3D) static and dynamic analysis of thick plates based on the Meshless Local Petrov-Galerkin (MLPG) is presented. Using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a uni...

Abstract. Two optimal monotone integral principles (equivalently for the Laplacian, two sharp iso-weighted-volume inequalities) are established through extending the first and second integral bounds of H. Weinberger for the Green functions (i.e., fundamental solutions) of uniformly elliptic equations in terms of the layer-cake formula, a one-dimensional monotone integral principle, and the isop...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

In this paper we discuss the stability and instability properties of two classes of conservative dynamical systems which have two interconnected components: a nite-dimensional and an innnite-dimensional subsystem. The nite-dimensional component is a linear mechanical system with gyroscopic terms and it is coupled to a wave equation deened on an innnite spatial domain via two diierent types of c...

This paper presents a new approach based on the meshless local Petrov–Galerkin (MLPG) and collocation methods to treat the parabolic partial differential equations with non-classical boundary conditions. In the presented method, the MLPG method is applied to the interior nodes while the meshless collocation method is applied to the nodes on the boundaries, and so the Dirichlet boundary conditio...

Abstract: In this paper, we investigate piecewise approximate solution for linear two dimensional Volterra integral equation, based on the interval approximation of the true solution by truncated Chebyshev series. By discretization respect to spatial and time variables, the solution is approximated by using collocation method. Analysis of discretization error is discussed and efficiency of the ...

In this paper we derive a new handy integral equation for the free boundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a one-dimensional, regular diffusion X0,x. The new integral equation allows to explicitly find the free boundary b(·) in some so far unsolved cases, as when X0,x is a three-dimensional Bessel process or a ...

Using the collective field theory approach of large–N generalized two–dimensional Yang–Mills theory on cylinder, it is shown that the classical equation of motion of collective field is a generalized Hopf equation. Then, using the Itzykson–Zuber integral at the large–N limit, it is found that the classical Young tableau density, which satisfies the saddle–point equation and determines the large...