Computational simulation can be defined as any computer application which involves the numerical solution to a system of partial differential equations. In this paper, a broad overview is given of verification procedures for computational simulation. The two aspects of verification examined are code verification and solution verification. Code verification is a set of procedures developed to fi...

This report investigates a technique to calculate the distributions of discretization errors for a model of advection-diffusion-reaction with stochastic noise in problem data. The focus is on operator-split discretization methods. The error is decomposed into components due to the splitting and due to the discretization within each component. We present a method to estimate the distributions of...

This work deals with the numerical simulation of wave propagation on unbounded domains with localized heterogeneities. To do so, we propose to combine a discretization based on a discontinuous Galerkin method in space and explicit finite differences in time on the regions containing heterogeneities with the retarded potential method to account the unbounded nature of the computational domain. T...

We present a numerical method for the «-dimensional initial value problem for the scalar conservation law u{xx , ... , x„ , t)¡ + Y!¡=\ fi(u)x¡ = 0 , u(xx.Xn , 0) = «o(*i > • • • , xn). Our method is based on the use of dimensional splitting and Dafermos's method to solve the one-dimensional equations. This method is unconditionally stable in the sense that the time step is not limited by the s...

Abstract. Convergence of a full discretization is shown for a general class of nonlinear parabolic November 10, 2011 problems. The numerical method combines the backward Euler method for the time discretization with a generalized internal approximation scheme for the spatial discretization. The governing monotone elliptic differential operator is described by a nonlinearity that may have anisot...

This paper proposes an experimental evaluation of various discretization schemes in three different evolutionary systems for inductive concept learning. The various discretization methods are used in order to obtain a number of discretization intervals, which represent the basis for the methods adopted by the systems for dealing with numerical values. Basically, for each rule and attribute, one...

We introduce a uniformly convergent iterative method for the systems arising from non-symmetric IIPG linear approximations of second order elliptic problems. The method can be viewed as a block Gauß–Seidel method in which the blocks correspond to restrictions of the IIPG method to suitably constructed subspaces. Numerical tests are included, showing the uniform convergence of the iterative meth...

We present a numerical method for solving the system of equations of a model of cellular electrical activity that takes into account both geometrical effects and ionic concentration dynamics. A challenge in constructing a numerical scheme for this model is that its equations are stiff: There is a time scale associated with “diffusion” of the membrane potential that is much faster than the time ...

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

In this paper, we describe an efficient method for 3D image segmentation. The method uses a PDE model – the so called generalized subjective surface equation which is an equation of advection-diffusion type. The main goal is to develop an efficient and stable numerical method for solving this problem. The numerical solution is based on semi-implicit time discretization and flux-based level set ...