The Convergence of Spline Collocation for Strongly Elliptic Equations on Curves.
The equivalence of some integral equations and boundary value problems
The extended Adomian decomposition method for fourth order boundary value problems.
The Friedrichs extension of certain singular differential operators. II.
The Fučík spectra for multi-point boundary-value problems.
The generalized boundary value problem is a Fredholm mapping of index zero
In the paper it is proved that each generalized boundary value problem for the n-th order linear differential equation generates a Fredholm mapping of index zero.
The h, p and h-p Versions of the Finite Element Method in 1 Dimension. Part III. The Adaptive h-p Version.
The h, p and h-p Versions of the Finite Element Method in 1 Dimension. Part I. The Error Analysis of the p-Version.
The h, p and h-p Versions of the Finite Element Method in 1 Dimension. Part II. The Error Analysis of the h- and h-p Versions.
The inverse carrier problem
The problem was motivated by Borůvka’s definitions of the carrier and the associated carrier. The inverse carrier problem is precisely defined and partially solved. Examples are given.
The method of solution of the boundary value problem applied to a certain fourth order differential equation
The mixed problem for a degenerate operator equation.
The spectral approximation for the shock layer problems.
The structure of spline collocation matrix for singularly perturbation problems with two small parameters.
The Sturm-Liouville Friedrichs extension
The characterization of the domain of the Friedrichs extension as a restriction of the maximal domain is well known. It depends on principal solutions. Here we establish a characterization as an extension of the minimal domain. Our proof is different and closer in spirit to the Friedrichs construction. It starts with the assumption that the minimal operator is bounded below and does not directly use oscillation theory.
Three-point boundary value problem for nonlinear third-order differential equations with parameter
Transfer of boundary conditions for Poisson's equation on a circle
The method of transfer of boundary conditions yields a universal frame into which most methods for solving boundary value problems for ordinary differential equations can be included. The purpose of this paper is to show a possibility to extend the idea of transfer of conditions to a particular twodimensional problem.
Transfer of conditions for singular boundary value problems
Numerical solution of linear boundary value problems for ordinary differential equations by the method of transfer of conditions consists in replacing the problem under consideration by a sequence of initial value problems. The method of transfer for systems of equations of the first order with Lebesque integrable coefficients was studied by one of the authors before. The purpose of this paper is to extend the idea of the transfer of conditions to singular boundary value problems for a linear second-order...
Transformations of linear second order ordinary differential equations
Two point boundary value problems for linear third order differential equations in the Colombeau algebra