相关论文: A Finite Difference Scheme based on Cubic Trigonom…

In this paper we apply the boundary elements method (BEM) and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of two-dimensional time-fractional partial differential equations (TFPDEs). The fractional…

The aim of this work is to devise and analyse an accurate numerical scheme to solve Erd\'elyi-Kober fractional diffusion equation. This solution can be thought as the marginal pdf of the stochastic process called the generalized grey…

In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…

Propagation characteristics of a wave are defined by the dispersion relationship, from which the governing partial differential equation (PDE) can be recovered. PDEs are commonly solved numerically using the finite-difference (FD) method,…

The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis…

The variable two-step backward differentiation formula (BDF2) is revisited via a new theoretical framework using the positive semi-definiteness of BDF2 convolution kernels and a class of orthogonal convolution kernels. We prove that, if the…

This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…

This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…

In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…

The stochastic Cahn-Hilliard equation driven by a fractional Brownian sheet provides a more accurate model for correlated space-time random perturbations. This study delves into two key aspects: first, it rigorously examines the regularity…

A novel efficient and high accuracy numerical method for the time-fractional differential equations (TFDEs) is proposed in this work. We show the equivalence between TFDEs and the integer-order extended parametric differential equations…

In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while…

Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we…

We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved…

A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with…

In this article, we consider discrete schemes for a fractional diffusion equation involving a tempered fractional derivative in time. We present a semi-discrete scheme by using the local discontinuous Galerkin (LDG) discretization in the…

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…

In this paper, we develop two fast implicit difference schemes for solving a class of variable-coefficient time-space fractional diffusion equations with integral fractional Laplacian (IFL). The proposed schemes utilize the graded $L1$…

The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time-space dependent variable coefficients is challenging, especially when the classical weak initial singularities are…

In this article, we propose a higher order approximation to Caputo fractional (C-F) derivative using graded mesh and standard central difference approximation for space derivatives, in order to obtain the approximate solution of time…