In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

In this paper we propose a Bayesian method for estimating hyperbolic diffusion models. The approach is based on the Markov Chain Monte Carlo (MCMC) method after discretization via the Milstein scheme. Our simulation study shows that the hyperbolic diffusion exhibits many of the stylized facts about asset returns documented in the financial econometrics literature, such as a slowly declining aut...

We consider the oxygen diffusion equation. Oxygen diffusion in a sike cell with simultaneous absorption is an important problem. Oxygen diffusion has a wide range of medical applications. Numerical solutions of its partial differential equation are obtained by extrapolation method with the vector of values V approximating to C (diffusion) at the mesh points. And the results gave a good agreemen...

This study makes the first attempt to apply the Kansa method in the solution of the time fractional diffusion equations, in which the MultiQuadrics and thin plate spline serve as the radial basis function. In the discretization formulation, the finite difference scheme and the Kansa method are respectively used to discretize time fractional derivative and spatial derivative terms. The numerical...

In this paper, a class of alternating group explicit iterative parallel method(AGI) is derived for solving diffusion equations based on a high order implicit scheme. Also the convergence analysis and the stability analysis are given. In order to verify the results, several numerical examples are presented in the end of the paper. Mathematics Subject Classification: 65M06, 74S20

In this paper, we present a novel PDE based error concealment algorithm. We formulate the error concealment problem as a sequential optimization problem with both smoothing and orientation constraints. By introducing the orientation constraint we convert a nonlinear variational problem into a problem that is well posed and which can be solved without iterative operations. A modified orientation...