相关论文: An Operator Approach to the Integration of Linear …
We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…
The relations between solutions of the three types of totally linear partial differential equations of first order are presented. The approach is based on factorization of a non-homogeneous first order differential operator to products…
We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. We characterize the associated model by means of a generalized action for a scalar field, containing…
We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the…
In this article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to…
In this paper, we give a formulation of the variational iteration method that makes it suitable for the analysis of the solutions of Klein-Gordon equations with variable coefficients. We particularly study a Klein-Gordon problem which has…
We consider the Klein--Gordon equation associated with the Laplace--Beltrami operator $\Delta$ on real hyperbolic spaces of dimension $n\!\ge\!2$; as $\Delta$ has a spectral gap, the wave equation is a particular case of our study. After a…
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant…
Recently, reduced order modeling methods have been applied to solving inverse boundary value problems arising in frequency domain scattering theory. A key step in projection-based reduced order model methods is the use of a sesquilinear…
In this work we present a new approach for the implementation of operational Tau method for the solutions of linear differential and integral equations. In our approach we use the three terms relation of an orthogonal polynomial basis to…
We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…
This work introduces a methodology for generating linear operators that approximately represent nonlinear systems of perturbed ordinary differential equations. This is done through the application of classical perturbation theory via the…
We study the Dirichlet problem for semilinear equations on general open sets with measure data on the right-hand side and irregular boundary data. For this purpose we develop the classical method of orthogonal projection. We treat in a…
A new analytical operator method is discussed which solves linear ordinary differential equations with regular singularities. Solutions are obtained in analytic series form and also in Mellin-Barnes-type contour integral form. Exact series…
We suggest method based on the skeleton decomposition of linear operators in order to reduce ill-posed degenerate differential equations to the non-classic initial-value problem enjoying unique solution
In this paper we generalize the fermionic approach to the KP hierarchy sudgested in the papers of Kyoto school 1981-1984 (Sato,Jimbo, Miwa...). The main idea is that the components of the intertwiningoperators are in some sense a…
The numerical approximation of the semilinear Klein--Gordon equation in the $d$-dimensional space, with $d=1,2,3$, is studied by analyzing the consistency errors in approximating the solution. By discovering and utilizing a new cancellation…
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…