*Correspondence: [email protected] Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solution...

Aim of the paper is to investigate approximate analytical solution of time-dependent partial differential equation using a semi-analytical method, the Optimal Homotopy Asymptotic Method (OHAM). To show the efficiency of the proposed method, we consider one-dimensional heat and advection-diffusion equations. OHAM uses simple computations with pretty good enough approximate solution, which has an...

This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by g x, t I t 1 − R μe−μx while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discus...

Semi-analytical solutions for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation with arbitrary boundary conditions are derived by developing Galerkin strip distributed transfer function method. Based on the nonlocal elasticity theory for piezoelectric materials and Hamilton's principle, the governing equations of motion and boundary conditions are ...

in this study, the stability problem of a circular orthotropic cylindrical shell under the effect of anaxial compression varying with a power function of time is considered. at first, the modified donnell typedynamic stability and compatibility equations are obtained using love’s shell theory. applying the galerkinmethod and rayleigh-ritz variational techniques to these equations and taking the...

in almost all of the present mathematical models, the upstream subbasins, with overland flow as the dominant type of flow, are simulated as a rectangular plane. however, the converging plane is the closest shape to an actual upstream subbasin. the intricate nature of the governing equations of the overland flow on a converging plane is the cause of prolonged absence of an analytical or semi ana...

In this paper, the problem of forced convection over a horizontal flat plate under condition of variable plate temperature is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. This paper provides good supplements to the existing literature and generalizes the previ...