Related papers: The factorization and simulation for fundamental s…

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…

We consider the Cauchy problem associated with a general parabolic partial differential equation in $d$ dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as…

Within the framework of the previous paper [8]. we develop a generalized stochastic calculus for processes associated to higher order diffusion operators. Applications to the study of a Cauchy problem, a Feynman-Kac formula and a…

We apply the Monte Carlo method to solving the Dirichlet problem of linear parabolic equations with fractional Laplacian. This method exploit- s the idea of weak approximation of related stochastic differential equations driven by the…

In this paper, we develop fast procedures for solving linear systems arising from discretization of ordinary and partial differential equations with Caputo fractional derivative w.r.t time variable. First, we consider a finite difference…

We construct and study a fundamental solution of Cauchy's problem for p-adic parabolic equations of a certain the type. The fundamental solution is the transition density of a p-adic Markov process.

In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…

We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix…

The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive. The basic idea of the factorization method applied on such a system is to control…

In this paper, we present a general scheme to construct integrable systems based on realization in the coboundary dynamical Poisson groupoids of Etingof and Varchenko. We also present a factorization method for solving the Hamiltonian…

We investigate the Cauchy problem for a semilinear spatio--temporal fractional diffusion equation with a time-dependent forcing term: \[ \partial_t^\alpha u + (-\Delta)^{\mathsf{s}} u = |u|^p + t^{\sigma}\,\mathbf{w}(x), \quad (t,x) \in…

We study the Cauchy problem for the advection-diffusion equation $\partial_t u + \mathrm{div} (u b ) = \Delta u$ associated with a merely integrable divergence-free vector field $b$ defined on the torus. We discuss existence, regularity and…

Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures…

The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…

This paper proposes a new theory and methodology to tackle the problem of unifying distributed analyses and inferences on shared parameters from multiple sources, into a single coherent inference. This surprisingly challenging problem…

The Picard-Lefschetz theory has been attracting much attention as a tool to evaluate a multi-variable integral with a complex weight, which appears in various important problems in theoretical physics. The idea is to deform the integration…

The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…

We address the possibility of performing numerical Monte Carlo simulations for the thermodynamics of quantum dissipative systems. Dissipation is considered within the Caldeira-Leggett formulation, which describes the system in the…

We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…

A general synthetic iterative scheme is proposed to solve the Enskog equation within a Monte Carlo framework. The method demonstrates rapid convergence by reducing intermediate Monte Carlo evolution and preserves the asymptotic-preserving…