In this paper, a moving mesh technique and a non-standard finite difference method are combined, and a moving mesh non-standard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm ...

The scope of this study is to establish an effective approximation method for linear first order singularly perturbed Volterra-Fredholm integro-differential equations. finite difference scheme constructed on Shishkin mesh by using appropriate interpolating quadrature rules and exponential basis function. recommended second convergent in the discrete maximum norm. Numerical results illustrating ...

In this paper, we consider the local discontinuous Galerkin method (LDG) for solving singularly perturbed convection-diffusion problems in oneand two-dimensional settings. The existence and uniqueness of the LDG solutions are verified. Numerical experiments demonstrate that it seems impossible to obtain uniform superconvergence for numerical fluxes under uniform meshes. Thanks to the implementa...

This paper describes a new technique for the triangulation of parametric surfaces. Most earlier methods sample the parameter domain, and the wrong choice of parameterization can spoil the triangulation or even cause the algorithm to fail. Conversely, we use a local tessellation primitive to sample and triangulate the surface. The sampling is almost uniform and the parameterization becomes irrel...

The following article investigates buckling of moderately thick circular Nano plates with an orthotropic property under uniform radial compressive in-plane mechanical load. Taking into account nonlocal elasticity theory (Eringen), principle of virtual work, first order shear deformation plate theory (FSDT) and nonlinear Von-Karman strains, the governing equations are obtained based on displacem...

Abstract A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed the data so that only regular exponential boundary layers appear in solution. domain decomposition used, which uses a rectangular grid outside layer and Shishkin mesh, aligned curvature of outflow boundary, near layer. Numerical results ...

This paper deals with a more general class of singularly perturbed boundary value problem for a differential-difference equations with small shifts. In particular, the numerical study for the problems where second order derivative is multiplied by a small parameter ε and the shifts depend on the small parameter ε has been considered. The fitted-mesh technique is employed to generate a piecewise...

In this research, the finite difference method is used to solve initial value problem of linear first order Volterra-Fredholm integro-differential equations with singularity. By using implicit rules and composite numerical quadrature rules, scheme established on a Shishkin mesh. The stability convergence proposed are analyzed two examples solved display advantages presented technique.