There have been several recent works on developing moving mesh methods for solving phase-field equations. However, it is observed that some of these moving mesh solutions are essentially different with the solutions on very fine fixed meshes. One of the purposes of this work is to understand the reason for the differences. We carried out numerical sensitivity studies systematically in this pape...

LASATER, MATTHEW SCOTT. Numerical Methods for the Wigner-Poisson Equa-tions. (Under the direction of C.T. Kelley).This thesis applies modern numerical methods to solve the Wigner-Poisson equa-tions for simulating quantum mechanical electron transport in nanoscale semicon-ductor devices, in particular, a resonant tunneling diode (RTD). The goal of thisdissertation is to provi...

The heat-bal ance in te gral method is used to solve the non-lin ear heat dif fu sion equa tion in static tur bu lent superfluid he lium (He II). Al though this is an ap prox i mate method, it has proven that it gives so lu tions with fairly good ac cu racy in non-lin ear fluid dy nam ics and heat trans fer. Us ing this method, it has been pos si ble to de velop pre dic tive so lu tions that re...

In this paper we treat three problems on a two-dimensional ‘punctured periodic domain’: we take Ωr = (−L,L) \Dr, where Dr = B(0, r) is the disc of radius r centred at the origin. We impose periodic boundary conditions on the boundary of the box Ω = (−L,L), and Dirichlet boundary conditions on the circumference of the disc. In this setting we consider the Poisson equation, the Stokes equations, ...

We give a systematic account of isospectral deformations for Sturm-Liouville and Dirac-type operators and associated hierarchies of nonlinear evolution equations. In particular, we study generalized KdV and modified KdV-hierarchies and their reduction to the standard (m)KdV-hierarchy. As an example we study the Harry Dym equation in some detail and relate its solutions to KdV-solutions and to H...

in this paper, an analytical method called the parametric iteration method (pim) is presented for solving the second-order singular ivps of lane-emden type, and its local convergence is discussed. since it is often useful to have an approximate analytical solution to describe the lane-emden type equa- tions, especially for ones where the closed-form solutions do not exist at all, therefore, an ...

In this paper we will present a numerical method for computing incompressible free surface ows in irregular ge ometries in three dimensions The approach we are taking is based on three ideas The rst is the second order ac curate projection method of Bell Colella and Glaz Bell et al for computing nite di erence approximations to the incompressible ow equations on rectangular grids The second is ...

results for error analysis of finite element methodWe consider the following four problems: 1:(E)w: Find u ∈ V such thata(u, v) = (f, v) for all v ∈ V .2:(Eh)w: Find uh ∈ Vh such thata(uh, vh) = (f, vh) for all vh ∈ Vh.3:(E)w: Find u ∈ V such thata (u , v) = (f, v) for all v ∈ V . DDM APPLIED TO RADIATION PROBLEMS389 4:(Eh )w: Find u Nh ∈ Vh such ...

Joint estimation of unknown model parameters and unobserved state componentsfor stochastic, nonlinear dynamic systems is customarily pursued via the extendedKalman filter (EKF). However, in the presence of severe nonlinearities in the equa-tions governing system evolution, the EKF can become unstable and accuracy ofthe estimates gets poor. To improve the results, in this paper w...

Synopsis This article argues that first semester calculus courses for non-mathematics majors should be taught using infinitesimals. This applies to both high school and undergraduate calculus courses. The use of infinitesimals in calculus, though more intuitive than the approach developed in the 19 th century, has been controversial for over two millennia. However, in the 20 th century their us...