A generalized inverse problem for a two-dimensional difference operator is introduced. Two operators, for which such a problem is solved (we call such operators algebro-geometric), are found.

in this paper we investigate a nonlinear evolution model described by the rosenau-kdv equation. we propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of o(τ2 + h2). furthermore we show the existence and uniqueness of numerical solutions. comparing the numerical results with other methods in...

of the ordinary differential equation which occurs in the boundary condition. An exact nonreflecting boundary condition was derived previously for use with the time dependent wave equation in three Finally, we shall solve a sequence of scattering problems space dimensions. Here it is shown how to combine that boundary by using an explicit finite difference method and our condition with finite d...

A finite volume scheme is discussed for discretizing diffusion operators. Both cell-center unknowns and cell-vertex unknowns are used originally in the construction of the finite volume scheme. Then cell-vertex unknowns are eliminated by expressing them locally as linear combinations of cell-center unknowns, which is derived by the following process. First we construct a special control-volume ...

The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for...

A stable hybrid method for hyperbolic problems that combines the unstructured finite volume method with high-order finite difference methods has been developed. The coupling procedure is based on energy estimates and stability can be guaranteed. Numerical calculations verify that the hybrid method is efficient and accurate.

In this paper, transient thermomechanical stress intensity factors for functionally graded cylinders with complete internal circumferential cracks are obtained using the weight function method. The finite difference method is used to calculate the time dependent temperature distribution and thermal stresses along the cylinder thickness. Furthermore, finite element analysis is performed to deter...

A linear-implicit finite difference scheme is given for the initial-boundary problem of GBBMBurgers equation, which is convergent and unconditionally stable. The unique solvability of numerical solutions is shown. A priori estimate and second-order convergence of the finite difference approximate solution are discussed using energy method. Numerical results demonstrate that the scheme is effici...

An adaptive finite difference method for first order nonlinear systems of ordinary differential equations subject to multipoint nonlinear boundary conditions is presented. The method is based on a discretization studied earlier by H. B. Keller. Variable order is provided through deferred corrections, while a built-in natural asymptotic estimator is used to automatically refine the mesh in order...

This paper examines formulation of the discretization schemes for diffusion process simulation that allow coarse grid spacings in the areas of exponentially varying concentrations and fluxes. The method of integral identities is used as a common framework for exponential fitting of both the finite difference and finite element schemes. An exponentially fitted finite difference scheme, with disc...