in this article, the discrete time state space model with first-order autoregressive dependent process noise is considered and the recursive method for filtering, prediction and smoothing of the hidden state from the noisy observation is designed. the explicit solution is obtained for the hidden state estimation problem. finally, in a simulation study, the performance of the designed method ...

Discrete autocorrelation wavelets have recently been applied in the statistical analysis of locally stationary time series. This form of time series analysis also requires the construction of the inner product matrix of such wavelets. To date, both discrete autocorrelation wavelets and the inner product matrix have been constructed via a brute force technique which proves to be computationally ...

Discrete autocorrelation (a.c.) wavelets have recently been applied in the statistical analysis of locally stationary time series for local spectral modelling and estimation. This article proposes a fast recursive construction of the inner product matrix of discrete a.c. wavelets which is required by the statistical analysis. The recursion connects neighbouring elements on diagonals of the inne...

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani, Tucsnak and Weiss [24]. Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE’s. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provi...

A high-order leap-frog based non-dissipative discontinuous Galerkin timedomain method for solving Maxwell’s equations is introduced and analyzed. The proposed method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements, with a N th-order leap-frog time scheme. Moreover, the interpolation degree is defined at the element level and the mesh ...

Oil production may be accompanied by Sand Production (SP) in the weak sandstone reservoirs. Fluid flow is an important factor in transporting the separated grains and completing the SP mechanism. In this paper, the effect of fluid parameters, fluid flow, and fluid pressure on the SP is investigated by applying the Discrete Element Method (DEM). Parametric studies show that fluid velocity is red...

Rock slope stability depends very much on the strength features of the rock and the geometrical and strength characteristics of the discontinuities (e.g., roughness, wall strength and persistence). Since a rock mass is not a continuum, its behavior is dominated by such discontinuities as faults, joints and bedding planes. Also, Rock slope instability is a major hazard for human activities and o...

We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an artificial dissipation that is defined so that any convex invariant sets containing the initial data is an invariant domain for the method. The invariant do...