Contingent solutions to the center manifold equation
Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies
In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of the limiting...
Convergence analysis of finite difference schemes for semi-linear initial-value problems
Convergence dans de la solution de l’équation de Klein-Gordon vers celle de l’équation des ondes
Convergence of a difference method for a system of first order partial differential equations of hyperbolic type
Convergence of a finite element method based on the dual variational formulation
Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem
We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the scheme, which appears...
Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem
We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the scheme, which appears...
Convergence of iterative methods applied to generalized Fisher equation.
Convergence results for unbounded solutions of first order non-linear differential-functional equations
We consider the Cauchy problem in an unbounded region for equations of the type either or . We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.
Curved triangular finite -elements
Curved triangular -elements which can be pieced together with the generalized Bell’s -elements are constructed. They are applied to solving the Dirichlet problem of an elliptic equation of the order in a domain with a smooth boundary by the finite element method. The effect of numerical integration is studied, sufficient conditions for the existence and uniqueness of the approximate solution are presented and the rate of convergence is estimated. The rate of convergence is the same as in the...
Das Iterationsverfahren für eine partielle Differentialgleichung vierter Ordnung
Decaying Entire Positive Solutions of Quasilinear Elliptic Equations.
Derivation of the Zakharov equations
Difference inequalities of the elliptic type
Discrete differential operators in multidimensional Haar wavelet spaces.
Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications
Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerical methods, we use large time-steps to achieve long simulation times of about 10 000 years. We propose...
Doubly nonlinear parabolic equations related to the -Laplacian operator: Semi-discretization.
Editorial comment on the paper Huashui Zhan, Junning Zhao: Some remarks on Prandtl system
Electromagnetic scattering at composite objects : a novel multi-trace boundary integral formulation
Since matrix compression has paved the way for discretizing the boundary integral equation formulations of electromagnetics scattering on very fine meshes, preconditioners for the resulting linear systems have become key to efficient simulations. Operator preconditioning based on Calderón identities has proved to be a powerful device for devising preconditioners. However, this is not possible for the usual first-kind boundary formulations for electromagnetic...