Two-point boundary value problems for a system of nonlinear first order ordinary differential equations are considered. It was shown in former papers of the authors that starting from the two-point exact difference scheme (EDS) one can derive a so-called truncated difference scheme (TDS) which possesses a prescribed order of accuracy O(|h|m) w.r.t. the maximal step size |h|. This m-TDS represen...

We present a method for solving nonlinear reaction-diiusion equations, s @p @t ? r (Krp) = f (p); using a mixed nite-element method. To linearize the mixed-method equations , we use a two-grid scheme that relegates all of the Newton-like iterations to grids much coarser than the original one, with no loss in order of accuracy. The use of a multigrid-based solver for the indeenite linear systems...

Two techniques for reliably controlling the defect (residual) in the numerical solution of nonstiff initial value problems were given in [D. This work describes an alternative approach based on Hermite-Birkhoff interpolation. The new approach has two main advantagesmit is applicable to Runge-Kutta schemes of any order, and it gives rise to a defect of the optimum asymptotic order of accuracy. F...

Keywords: Elliptic equations Nonlocal boundary value problems Difference schemes Stability a b s t r a c t The well-posedness of the Bitsadze–Samarskii type nonlocal boundary value problem in Hölder spaces with a weight is established. The coercivity inequalities for the solution of the nonlocal boundary value problem for elliptic equations are obtained. The stable second order of accuracy diff...

We develop two-grid schemes for solving nonlinear reaction-diiusion systems , @p @t ? r (Krp) = f(x; p); where p = (p; q) is an unknown vector-valued function. The schemes use discretizations based on a mixed nite-element method. The two-grid approach yields iterative procedures for solving the nonlinear discrete equations. The idea is to relegate all of the Newton-like iterations to grids much...

The possibility that Lorentz symmetry is violated in gravitational processes is relatively unconstrained by experiment, in stark contrast with the level of accuracy to which Lorentz symmetry has been confirmed in the matter sector. One model of Lorentz violation in the gravitational sector is Einstein-aether theory, in which Lorentz symmetry is broken by giving a vacuum expectation value to a d...

In this paper, we introduce a general approach for proving optimal L2 error estimates for the semi-discrete local discontinuous Galerkin (LDG) methods solving linear high order wave equations. The optimal order of error estimates hold not only for the solution itself but also for the auxiliary variables in the LDG method approximating the various order derivatives of the solution. Several examp...

This paper considers the application of the method of boundary penalty terms (“SAT”) to the numerical solution of the wave equation on complex shapes with Dirichlet boundary conditions. A theory is developed, in a semi-discrete setting, that allows the use of a Cartesian grid on complex geometries, yet maintains the order of accuracy with only a linear temporal error-bound. A numerical example,...

In (Xu and Shu in J. Sci. Comput. 40:375–390, 2009), a local discontinuous Galerkin (LDG) method for the surface diffusion of graphs was developed and a rigorous proof for its energy stability was given. Numerical simulation results showed the optimal order of accuracy. In this subsequent paper, we concentrate on analyzing a priori error estimates of the LDG method for the surface diffusion of ...

Background and Objective: Intraoperative consultation by frozen section is a high – risk procedure with important consequences. Therefore, it is critical to determine efficiency of frozen section performance periodically. This study was performed to determine the accuracy of frozen section in Urmia University of Medical Sciences. Materials & Methods:Inthis cross sectional study, we compared th...