Related papers: Solving Fredholm integro-differential equations us…
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
Motivated by Fredholm theory, we develop a framework to establish the convergence of spectral methods for operator equations $\mathcal L u = f$. The framework posits the existence of a left-Fredholm regulator for $\mathcal L$ and the…
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical tra jectory remains at least uni-…
The transport of energy through radiation is very important in many astrophysical phenomena. In dynamical problems the time-dependent equations of radiation hydrodynamics have to be solved. We present a newly developed…
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
This paper addresses the challenging numerical simulation of nonlinear hybrid stochastic functional differential equations with infinite delays. We first propose an explicit scheme using space and time truncation, requiring only finite…
We describe a first attempt to calculate scalar 2-loop box-functions with arbitrary internal masses, applying a novel method proposed in hep-ph/9407234. Four of the eight integrals are accessible to integration by means of the residue…
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector…
In this paper, we propose a new finite element approach, which is different than the classic Babuska-Osborn theory, to approximate Dirichlet eigenvalues. The Dirichlet eigenvalue problem is formulated as the eigenvalue problem of a…
We prove the Fredholm alternative for a class of two-dimensional first-order hyperbolic systems with periodic-Dirichlet boundary conditions. Our approach is based on a regularization via a right parametrix.
In this paper we discuss a framework for the polynomial approximation to the solution of initial value problems for differential equations. The framework, initially devised for the approximation of ordinary differential equations, is…
The most general situation of the reinforcement of a plate with multiple holes by several patches is considered. There is no restriction on the number and the location of the patches. Two types of the patch attachment are considered: only…
We propose a hybrid approach to solve the high-frequency Helmholtz equation with point source terms in smooth heterogeneous media. The method is based on the ray-based finite element method (ray-FEM), whose original version can not handle…
The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct Fredholm modules on post critically finite fractals by regular harmonic structures. The modules are…
We devise an explicit method for computing combinatorial formulae for Hadamard products of certain rational generating functions. The latter arise naturally when studying so-called ask zeta functions of direct sums of modules of matrices or…
The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…
A simple yet effective numerical method using orthogonal hybrid functions consisting of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal triangular functions is proposed to solve numerically fractional…
We introduce a two-phase approximation method designed to resolve singularities in three-dimensional harmonic Dirichlet problems. The approach utilizes the classical Green's function representation, decomposing the function into its…
We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd (HHL) algorithm for solving a system of linear equations. In our hybrid scheme, a classical information feed-forward is required from the quantum phase estimation…
We establish precise convergence rates for semi-discrete schemes based on Radial Basis Function interpolation, as well as approximate approximation results for such schemes. Our schemes use stationary interpolation on regular grids, with…