Zdzislaw Kamont

Monotone iterative methods for impulsive hyperbolic differential-functional equations

Theorems on impulsive hyperbolic differential-functional inequalities are considered. Comparison results and a uniqueness criterion are obtained. A method of approximation of the solutions of impulsive hyperbolic differential-functional equations by means of solutions of the associated linear problems is established. The difference between the exact and the approximate solutions is estimated.

Numerical methods for hyperbolic functional differential problems on the Haar pyramid

Abstract.In this paper we prove relations between the eigenvalues of matrices that occur during the solution of linear programming problems with interior-point methods. We will present preconditioners for these matrices that preserve the relations and discuss the practical implications of our results when iterative linear solvers are used.

Functional Integral Equations

Let X be an arbitrary Banach space with the norm ∥·∥. We denote the Euclidean norm in R n and the norm in the Banach space X by the same symbol. Elements of the space R n will be denoted by x = (x1, …, x n ), s = (s1, …, s n ). Let E ⊂ R + n be a compact set and G(x) = }ξ ∈ E:ξ≤x}. Assume that functions

Comparison principles for impulsive hyperbolic equations of first order

E \in C\left( {E \times {X^m} \times X,\,X} \right),\;f = \left( {{f_1}, \ldots, \,{f_m}} \right) \in C\left( {E \times E \times X,\,{Y^m}} \right),\;\beta \in C\left( {E,\,E} \right),\;\alpha = \left( {{\alpha_1}, \ldots, {\alpha_m}} \right) \in C\left( {E,\,{E^m}} \right)

Periodic boundary value problem for impulsive hyperbolic partial differential equations of first order

are given and β(x) ≤ x, α i (x) ≤ x, 1 ≤ i ≤ m, for x ∈ E. Suppose that the sets H j (x) ⊂ G(x) for x ∈ E, 1 ≤ j ≤ m, are given. We assume further that H j (x) is contained in a p j — dimensional hyperplane, 1 ≤ p j ≤ n, parallel to the coordinate axes, and it is Lebesgue — measurable, considered as a p j — dimensional set. Let L Pj (H j (x)) denotes the p j — dimensional Lebesgue measure of H j (x). We assume that p j does not depend on x. If the p j — dimensional hyperplane containing the set H j (x) and being parallel to the coordinate axes is defined by the equations

Differential and difference inequalities generated by mixed problems for hyperbolic functional differential equations with impulses

{x_{{{t_1}}}} = {\bar{x}_{{{t_1}}}},\;{x_{{{t_2}}}} = {\bar{x}_{{{t_2}}}}, \ldots, \,{x_{{{t_r}}}} = {\bar{x}_{{{t_r}}}},\;r = n - {p_j},