Marchuk identity-type second order difference schemes of 2-d and 3-d elliptic problems with intersected interfaces
Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation
Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock version...
Matrix transformation method of approximate solution of partial differential equations
Méthodes numériques pour les équations de Navier-Stokes instationnaires des fluides visqueux incompressibles
Mimetic finite differences for elliptic problems
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent norm are derived.
Mimetic finite differences for elliptic problems
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H1 norm are derived.
Modelling macrophage infiltration into avascular tumours.
Monotone finite difference domain decomposition algorithms and applications to nonlinear singularly perturbed reaction-diffusion problems.
Monotone Iterative Methods for Finite Difference System of Reaction-Diffusion Equations.
Monotone methods for solving a boundary value problem of second order discrete system.
Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes
In this paper we present some recent results concerning convergence rate estimates for finite-difference schemes approximating boundary-value problems. Special attention is given to the problem of minimal smoothness of coefficients in partial differential equations necessary for obtaining the results.