r. ewing, o. liev, r. lazarov and a. naumovich in [1] proposed a finite volume discretization for one dimensional biot poroelasticity system in multilayer domains. their discretization and exact solution are invalid. we derive valid discretization and exact solution. finally, our numerical solution is compared with known exact solution in discrete l2 norm.

‎Linear semi-infinite programming problem is an important class of optimization problems which deals with infinite constraints‎. ‎In this paper‎, ‎to solve this problem‎, ‎we combine a discretization method and a neural network method‎. ‎By a simple discretization of the infinite constraints,we convert the linear semi-infinite programming problem into linear programming problem‎. ‎Then‎, ‎we use...

We analyze a numerical algorithm for solving radiative transport equation with vacuum or reflection boundary condition that was proposed in [4] with angular discretization by finite element method and spatial discretization by discontinuous Galerkin or finite difference method.

boundary integral equations (bie) are reformulations of boundary value problems for partial differential equations. there is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. in this paper, the neumann problem is reformulated to a bie, and then moving least squares as a meshless method is describe...

In this paper we discuss the numerical solution of initial-boundary value problem for the fourth order parabolic partial integro-differential equation. We use the forward Euler scheme for time discretization and the quasi-wavelet method for space discretization. Sometimes, we give a new method about the treatment of boundary condition. Numerical experiment is included to demonstrate the validit...

The time discretization of a very high-order finite volume method may give rise to new numerical difficulties resulting into accuracy degradations. Indeed, for the simple onedimensional unstationary convection-diffusion equation for instance, a conflicting situation between the source term time discretization and the boundary conditions may arise when using the standard Runge-Kutta method. We p...

We present a higher order accurate discontinuous Galerkin finite element method for the simulation of linear free-surface gravity waves. The method uses the classical Runge-Kutta method for the time discretization of the free-surface equations and the discontinuous Galerkin method for the space discretization. In order to circumvent numerical instabilities arising from an asymmetric mesh a stab...

A numerical procedure to determine the discrete conformai mapping of an arbitrary simply connected region onto the open unit disk is described. The method is fast and directly provides an estimate of the global error due to the discretization of the mapping. The intimate relationship between the Riemann Mapping Theorem and the numerical method of construction of the conformai mapping is brought...

We discuss problems associated with induction of decision rules from data with numerical attributes. Real-life data frequently contain numerical attributes. Rule induction from numerical data requires an additional step called discretization. In this step numerical values are converted into intervals. Most existing discretization methods are used before rule induction, as a part of data preproc...

In this article, we investigate numerical schemes for solving a three component CahnHilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three d...