Nonlinear stability and convergence of finite-differnce methods for the "good" Boussinesq equation.
Numerical analysis of nonlinear model of excited carrier decay
This paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved....
Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy.
Numerical approaches to rate-independent processes and applications in inelasticity
A conceptual numerical strategy for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The novelty is that we obtain convergence of subsequences of space-time discretizations even in case where the limit problem does not have a unique solution and we need no additional assumptions on higher regularity of the limit solution. The variety of general perspectives thus obtained is illustrated on several...
Numerical approximation of the non-linear fourth-order boundary-value problem
We consider functionals of a potential energy corresponding to . We are dealing with with . Various types of the subsoil of the plate are described by various types of the nonlinear term . The aim of the paper is to find a suitable computational algorithm.
Numerical computations for solidification problems with change of volume
Numerical identification of a coefficient in a parabolic quasilinear equation
In the article the following optimal control problem is studied: to determine a certain coefficient in a quasilinear partial differential equation of parabolic type so that the solution of a boundary value problem for this equation would minimise a given integral functional. In addition to the design and analysis of a numerical method the paper contains the solution of the fundamental problems connected with the formulation of the problem in question (existence and uniqueness of the solution of...
Numerical modeling of neutron flux in hexagonal geometry
Numerical modeling of the simultaneous heat and moisture transfer
Numerical modelling of river flow (numerical schemes for one type of nonconservative systems
In this paper we propose a new numerical scheme to simulate the river flow in the presence of a variable bottom surface. We use the finite volume method, our approach is based on the technique described by D. L. George for shallow water equations. The main goal is to construct the scheme, which is well balanced, i.e. maintains not only some special steady states but all steady states which can occur. Furthermore this should preserve nonnegativity of some quantities, which are essentially nonnegative...
Numerical simulation of tridimensional electromagnetic shaping of liquid metals.
Numerical solution of amixed problem for a polywave equation of Mangeron.
Numerical solution of boundary value problems by means of B-splines
Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method
Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.In the present paper we solve space-time fractional diffusion-wave equation with two space variables, using the matrix method. Here, in particular, we give solutions to classical diffusion and wave equations and fractional diffusion and wave equations with different combinations of time and space fractional derivatives. We also plot some graphs for these problems with the help of MATLAB routines.
Numerical solution of nonlinear diffusion with finite extinction phenomenon.
Numerical study of free interface problems using boundary integral methods.