Related papers: On classification of singular matrix difference eq…
We study second-order divergence-form systems on half-infinite cylindrical domains with a bounded and possibly rough base, subject to homogeneous mixed boundary conditions on the lateral boundary and square integrable Dirichlet, Neumann, or…
In an attempt to solve Maxwell's first order system of equations, starting from a given initial state, it is found that a consistent solution depending on the temporal evolution of the sources cannot be calculated. The well known retarded…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
This paper presents the non-linear generalization of a previous work on matrix differential models. It focusses on the construction of approximate solutions of first-order matrix differential equations Y'(x)=f(x,Y(x)) using matrix-cubic…
The paper presents theorems on the calculation of the index of a singular point and at the infinity of monotone type mappings. These theorems cover basic cases when the principal linear part of a mapping is degenerate. Applications of these…
We study existence and uniqueness of solutions for second order ordinary stochastic differential equations with Dirichlet boundary conditions on a given interval. In the first part of the paper we provide sufficient conditions to ensure…
This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…
In this work, a mixed problem for a time-fractional equation with a delayed argument and pseudodifferential operators related to Laplace operators with non-local boundary conditions in Sobolev classes is studied. The solutions to the…
Optimization problems with constraints in the form of a partial differential equation arise frequently in the process of engineering design. The discretization of PDE-constrained optimization problems results in large-scale linear systems…
A new problem is studied, the concept of exactness of a second order nonlinear ordinary differential equations is established. A method is constructed to reduce this class into a first order equations. If the second order equation is not…
Motivated by dimension reduction in regression analysis and signal detection, we investigate the order determination for large dimension matrices including spiked models of which the numbers of covariates are proportional to the sample…
We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The…
This paper is devoted to the study of the singularly perturbed second order partial integro-differential equations. The estimation of the solutions of Cauchy problem is obtained.
Since the order of elliptic type model equation (Laplace equation) is two [1], [2], then it is natural the order of composite type model equation must be [3] [4] [5] three. At each point of the domain under consideration these equations…
Modular and quasimodular solutions of specific second order differential equation in the upper-half plane which originates from a study of supersingular j-invariants are given explicitly. A characterization of the differential equation is…
Singular equations with rank-deficient Jacobians arise frequently in algebraic computing applications. As shown in case studies in this paper, direct and intuitive modeling of algebraic problems often results in nonisolated singular…
Issues concerning intelligent data analysis occurring in machine learning are investigated. A scheme for synthesizing correct supervised classification procedures is proposed. These procedures are focused on specifying partial order…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition…
We prove an existence result for a quasilinear elliptic equation satisfying natural growth conditions. As a consequence, we deduce an existence result for a quasilinear elliptic equation containing a singular drift. A key tool, in the…