Related papers: Solving Fredholm integro-differential equations us…
We show that with a few modifications the Adomian's method for solving second order differential equations can be used to obtain the known results of the special functions of mathematical physics. The modifications are necessary in order to…
A previously-developed hybrid particle-continuum method [J. B. Bell, A. Garcia and S. A. Williams, SIAM Multiscale Modeling and Simulation, 6:1256-1280, 2008] is generalized to dense fluids and two and three dimensional flows. The scheme…
We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form $H= \sum_{i=1}^K H_i = \sum_{i=1}^K H_{i_1} \otimes H_{i_2} \otimes \cdots \otimes H_{i_M}$. Given that the entries of all $\{ H_{i_1}, H_{i_2} ,…
A rational representation for the self--energy is explored to interpolate the solution of the Anderson impurity model in general orbitally degenerate case. Several constrains such as the Friedel's sum rule, positions of the Hubbard bands as…
The g-function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can be computed exactly in a form of the Fredholm determinant, but it is often hard to evaluate…
In this paper we study well posedness of a certain nonlinear Volterra-Fredholm dynamic integral and integro-dynamic equations on unbounded interval from arbitrary time scale. We derive the time scale analogue of certain integral…
This work is concerned with solving high-dimensional Fokker-Planck equations with the novel perspective that solving the PDE can be reduced to independent instances of density estimation tasks based on the trajectories sampled from its…
We present an integral equation approach to solving the Cahn-Hilliard equation equipped with boundary conditions that model solid surfaces with prescribed Young's angles. The discretization of the system in time using convex splitting leads…
In this work we initiate an integrability-based approach to multipoint conformal blocks for higher dimensional conformal field theories. Our main observation is that conformal blocks for $N$-point functions may be considered as…
In this paper a new method for computation of higher order corrections to the saddle point approximation of the Feynman path integral is discussed. The saddle point approximation leads to local Schr\"odinger problems around classical…
Solving Fredholm equations of the first kind is crucial in many areas of the applied sciences. In this work we adopt a probabilistic and variational point of view by considering a minimization problem in the space of probability measures…
This paper studies a family of convolution quadratures, a numerical technique for efficient evaluation of convolution integrals. We employ the block generalized Adams method to discretize the underlying initial value problem, departing from…
This paper analyzes three forms of representation of Boolean functions, such as Classical, Algebraic and Reed-Muller. The concept of intersection and subsets of representation forms have been introduced, moreover suitable criteria for…
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the…
We show how many classes of partial differential systems with local and nonlocal nonlinearities are linearisable in the sense that they are realisable as Fredholm Grassmannian flows. In other words, time-evolutionary solutions to such…
In this paper, we introduce the notions of semi-Bloch periodic functions and semi-anti-periodic functions. Stepanov semi-Bloch periodic functions and Stepanov semi-anti-periodic functions are considered, as well. We analyze the invariance…
In this paper the singular Emden-Fowler equation of fractional order is introduced and a computational method is proposed for its numerical solution. For the approximation of the solutions we have used Boubaker polynomials and defined the…
For 1-dimensional applications, Bude's method [Bude et al, Plasma Phys. Control. Fusion, 63 (2021) 035014] has been shown to be capable of accurately solving the all-FLR (Finite Larmor Radius) integro-differential wave equation as a…
In the present paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key of the construction is the bilinear forms and determinant structure of solutions of the SP equation. We also…
In this paper we construct high order numerical methods for solving third and fourth orders nonlinear functional differential equations (FDE). They are based on the discretization of iterative methods on continuous level with the use of the…