On a variant of the matrix transformation method for approximate solution of partial differential equations of second degree
On Composite Mesh Difference Methods for Hyperbolic Differential Equations.
On finite difference schemes of high order accuracy for elliptic equations with mixed derivatives
On monotone and Schwarz alternating methods for nonlinear elliptic PDEs
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...
On Monotone and Schwarz Alternating Methods for Nonlinear Elliptic PDEs
The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...
On multi-parameter error expansions in finite difference methods for linear Dirichlet problems
The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an -dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an (-dimensional) rectangular grid in the directions of the individual...
On preconditioning Schur complement and Schur complement preconditioning.
On projection-difference analogues of the identity operator
On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems.
On reducing bandwidth of matrices in the Go-Away algorithm for regular grids.
On Richardson Extrapolation for Finite Difference Methods on Regular Grids.
On shooting methods for the discrete Helmholtz equation with constant coefficients.
On Some High Accuracy Difference Schemes for Solving Elliptic Equations.
On the accuracy of multigrid truncation error estimates.
On the Construction of Finite Difference Schemes Approximating Generalized Solutions
On the convergence of a modified block SOR algorithm.
On the convergence of difference schemes for classical and weak solutions of the Dirichlet problem
On the Convergence of Finite Difference Scheme for Elliptic Equation With Coefficients Containing Dirac Distribution
On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations
Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov for finite difference...
On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman Equations
Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov for finite...