The spectral approximation for the shock layer problems.
The splitting in potential Crank–Nicolson scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip
We consider an initial-boundary value problem for a generalized 2D time-dependent Schrödinger equation (with variable coefficients) on a semi-infinite strip. For the Crank–Nicolson-type finite-difference scheme with approximate or discrete transparent boundary conditions (TBCs), the Strang-type splitting with respect to the potential is applied. For the resulting method, the unconditional uniform in time L2-stability is proved. Due to the splitting, an effective direct algorithm using FFT is developed...
The SQP method for control constrained optimal control of the Burgers equation
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...
The SQP method for control constrained optimal control of the Burgers equation
A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...
The stability analysis of a discretized pantograph equation
The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index. Furthermore, we show that the utilized proof technique enables us to investigate some other numerical formulae, too.
The Stability Function for Multistep Collocation Methods.
The stability of collocation methods for higher-order Volterra integro-differential equations.
The stability of collocation methods for VIDEs of second order.
The stability of Ritz-Volterra projection and error estimates for finite element methods for a class of integro-differential equations of parabolic type
In this paper we first study the stability of Ritz-Volterra projection (see below) and its maximum norm estimates, and then we use these results to derive some error estimates for finite element methods for parabolic integro-differential equations.
The steepest descent method for forward-backward SDEs.
The steepest-ascent method for the linear programming problem
The Stepwise Regression Algorithm Seen from the Statistician's Point of View
The strength of nonstationary iteration.
The strengthened C.B.S. inequality constant for second order elliptic partial differential operator and for hierarchical bilinear finite element functions
We estimate the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for hierarchical bilinear finite element spaces and elliptic partial differential equations with coefficients corresponding to anisotropy (orthotropy). It is shown that there is a nontrivial universal estimate, which does not depend on anisotropy. Moreover, this estimate is sharp and the same as for hierarchical linear finite element spaces.
The Strict Chebyshev Solution of Overdetermined Systems of Linear Equations with Rank Deficient Matrix
The strong pointwise convergence of nearest neighbor function fitting algorithm with applications to system identification
The structure of spline collocation matrix for singularly perturbation problems with two small parameters.
The structured distance to nearly normal matrices.
The structured distance to normality of an irreducible real tridiagonal matrix.
The structured sensitivity of Vandermonde-like systems.