相关论文: A New Perturbative Technique for Solving Integro-P…
We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original…
For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial index is considered. As a typical example we investigate an…
We present and compare three approaches for accurately retrieving depth-resolved temperature distributions within materials from their thermal-radiation spectra, based on: (1) a nonlinear equation solver implemented in commercial software,…
This paper introduces a novel methodology for solving distributed-order fractional differential equations using a physics-informed machine learning framework. The core of this approach involves extending the support vector regression (SVR)…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available and numerical methods are the main tools for approximating the…
The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional differential equations often have a singularity at the…
This article discusses the modeling of perturbed potential temperature in an atmospheric boundary layer. We adopt a convection-diffusion model with specified initial and boundary conditions that resulted from simplifying the linearized…
We develop a linear method for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. Our method, based on perturbation theory, is compared with heuristic linearizations of…
We study the diffusion equation with an appropriate change of variables. This equation is in general a partial differential equation (PDE). With the self-similar and related Ansat\"atze we transform the PDE of diffusion to an ordinary…
The work presents an integral solution of the time-fractional subdiffusion through a preliminary defined profile with unknown coefficients and the concept of penetration layer well known from the heat diffusion The profile satisfies the…
We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
A nonequilibrium distribution function of microscopic thermal current is studied by a direct numerical simulation in a thermal conducting steady state of particle systems. Two characteristic temperatures of the thermal current are…
In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we…
Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…