This paper will give the numerical difference scheme with Dirichlet boundary condition, and prove stability and convergence of the difference scheme, final numerical experiment results also confirm effectiveness of the algorithm. KeywordsFractional derivative; Numerical difference scheme; The gradient regularization method.

An optimal control problem for an elliptic variational inequality with a source term is considered. The obstacle is the control, and the goal is to keep the solution of the variational inequality close to the desired pro le while the H norm of the obstacle is not too large. The addition of the source term strongly a ects the needed compactness result for the existence of a minimizer.

We consider the problem of determining a pair of functions (u, f) satisfying the heat equation ut−∆u = φ(t)f(x, y), where (x, y) ∈ Ω = (0, 1)× (0, 1) and the function φ is given. The problem is ill-posed. Under a slight condition on φ, we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the interpolation method and the truncated Fourier se...

Background: Over the past decades, instruments and techniques of the transsphenoidal approach have improved greatly. All of these procedures, whether microscopic or endoscopic, must pass through the sphenoid sinus to reach the lesions. The sphenoid sinus is surrounded by several vital anatomical structures. Knowing the details of the anatomy of the sphenoid sinus and the extent of pneumatizatio...

Source term estimation (STE) of hazardous material (HAZMAT) releases is critical for emergency response. Such problem is usually solved with the aid of atmospheric dispersion modelling and inversion algorithms accompanied with a variety of uncertainty, including uncertainty in atmospheric dispersion models, uncertainty in meteorological data, uncertainty in measurement process and uncertainty i...

We consider the initial value problem for the equation u t = u xx +H(u), where H is the Heaviside graph, on a bounded interval with Dirichlet boundary conditions, and discuss existence, regularity and uniqueness of solutions and interfaces .

application of backward probability method in pollutant source tracking in non-uniform flow riversalireza ghanem.sc. student of water structures, tarbiat modares university, tehranmehdi mazaheri assistant prof., department of water structures, tarbiat modares university, tehranjamal mohammad vali samaniprofessor, department of water structures, tarbiat modares university, tehranintroductionriv...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...