4 FDM's for u ′ = f (t, u) 105 4.1 Convergence and stability of explicit, one step FDM's for u ′ =

Preface These lecture notes are intended to supplement a one-semester graduate-level engineering course at The George Washington University in numerical methods for the solution of partial differential equations. Both finite difference and finite element methods are included. The main prerequisite is a standard undergraduate calculus sequence including ordinary differential equations. In genera...

Introduction Conclusions References Tables Figures Back Close Full Screen / Esc This discussion paper is/has been under review for the journal Atmospheric Chemistry and Physics (ACP). Please refer to the corresponding final paper in ACP if available. Abstract Introduction Conclusions References Tables Figures Back Close Full Screen / Esc Abstract In cloud modeling studies, the time evolution of...

This paper focuses on a numerical analysis of a hard rock (ore) disintegration process. A bit moves into the ore and subsequently disintegrates it. The disintegration (i.e. fracture of ore) is solved via a deterministic approach (FEM) and a probabilistic approach (FEM in combination with the SBRA Simulation-Based Reliability Assessment method, i.e. Monte Carlo simulations, stochastic inputs). T...

, A numerical solution to the integro-differential equation describing the energy'distribution of a beam of electrons which has passed through matter, losing energy by radiation only, has been obtained utilizing a finite difference mesh method. Solutions were obtained for thicknesses of up to 0.1 radiation lengths for a complete screening approximation to the energy loss equation. The accuracy ...

This paper is concerned with the identification of the geometric structure of the boundary for a two-dimensional (stationary) elliptic equation. The domain identification problem is considered as a variational problem to minimize a defect functional, which utilizes some additional data on certain (known) parts of the boundary. The Gradient Projection Method is introduced for this problem and nu...

This paper presents an algorithm for solving interval linear programming(ILP) problems. Interval inequality constraints and equality constraints are discussed separately. The aim of the paper is to show that (ILP) problems can be decomposed into two general linear programming(LP) by the monotonicity of (LP) problems , and we can gain the interval objective values. Finally, the proposed method h...

In this paper, the authors consider the first boundary value problem for the nonlinear reaction diffusion equation: ut −∆um = αup1 in Ω, a smooth bounded domain in Rd(d ≥ 1) with the zero lateral boundary condition and with a positive initial condition, m ∈ ]0, 1[ (fast diffusion problem), α ≥ 0 and p1 ≥ m. Sufficient conditions on the initial data are obtained for the solution to vanish or bec...

We review numerical methods for computing eigenvalues of matrices. We start by considering the computation of the dominant eigenpair of a general dense matrix using the power method, and then generalize to orthogonal iterations and the QR iteration with shifts. We also consider divide-and-conquer algorithms for tridiagonal matrices. The second part of this survey involves the computation of eig...