In this paper, high order central finite difference schemes in a finite interval are analyzed for the diffusion equation. Boundary conditions of the initial-boundary value problem (IBVP) are treated by the simplified inverse Lax-Wendroff (SILW) procedure. For the fully discrete case, a third order explicit Runge-Kutta method is used as an example for the analysis. Stability is analyzed by both ...

Least-squares finite element methods (LSFEMs) for the inviscid Burgers equation are studied. The scalar nonlinear hyperbolic conservation law is reformulated by introducing the flux vector, or the associated flux potential, explicitly as additional dependent variables. This reformulation highlights the smoothness of the flux vector for weak solutions, namely f(u) ∈ H(div,Ω). The standard least-...

Chlorine is a widely used disinfectant and proxy for water quality (WQ) monitoring in distribution networks (WDN). Chlorine-based WQ regulation control aims to maintain pathogen-free water. residual evolution within WDN commonly modeled using the typical single-species decay reaction dynamics that account network-wide, spatiotemporal chlorine concentrations only. Prior studies have proposed mor...

Necessary and sufficient stability criteria for Friedrichs' scheme and the modified Lax-Wendroff scheme with smooth coefficients are derived by means of Kreiss' Matrix Theorem and the first Stability Theorem of Lax and Nirenberg. In this note we derive necessary and sufficient stability criteria for Friedrichs' scheme and the modified Lax-Wendroff scheme [8] for the hyperbolic system n (1) ". =...

is obtained where A (u) is the Jacobian matrix of the components of / with respect to the components of u. Equation (1.2) is said to be hyperbolic if the eigenvalues of the matrix pi + 6A are real for all real numbers m, 0. Several authors have proposed finite-difference schemes for the numerical integration of (1.1) (or (1.2)). In [6], Lax and Wendroff introduced an explicit scheme which is st...

this paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. the method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions.the construction of the nonstandard method is based on the special treatment of the interface using suitable jump condition...