Related papers: High-order fractional-compact finite difference me…
Finite difference methods (FDMs) are widely used for solving partial differential equations (PDEs) due to their relatively simple implementation. However, they face significant challenges when applied to non-rectangular domains and in…
The Kirchhoff plate model plays a vital role in modeling, computing and analyzing the mechanical behaviors of thin plate structures. This study propose a novel fourth-order multi-scale (FOMS) computational method for high-accuracy and…
In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffusion. The process arises from the interactions within the…
We study a second order scheme for spatial fractional differential equations with variable coefficients. Previous results mainly concentrate on equations with diffusion coefficients that are proportional to each other. In this paper, by…
A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…
In this paper, we develop a fast numerical method for solving the time-dependent Riesz space fractional diffusion equations with a nonlinear source term in the convex domain. An implicit finite difference method is employed to discretize…
In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…
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…
In this paper, we propose a novel recovery based finite element method for the Cahn-Hilliard equation. One distinguishing feature of the method is that we discretize the fourth-order differential operator in a standard $C^0$ linear finite…
In this work, fourth-order compact block-centered finite difference (CBCFD) schemes combined with the Crank-Nicolson discretization are constructed and analyzed for solving parabolic integro-differential type non-Fickian flows in…
This article focuses on the space-time isogeometric method for a linear time dependent fourth order problem. Using an auxiliary variable, first the problem is split into a system of two second order differential equations and then the…
We compute the rate of convergence of forward, backward and central finite difference $\theta$-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and…
We introduce suitable coordinate systems for pipes and their variants that allow us to transform partial differential equations (PDEs) on the pipe surfaces or in the solid pipes into computational domains with fixed limits/ranges. Such a…
In recent previous work [E. Hansen, T. Stillfjord and T. \r{A}berg, SIAM J. Numer. Anal., to appear], we analyzed the convergence of operator splitting methods applied to operator-valued differential Riccati equations (DRE). In this paper,…
We develop a finite difference approximation of order $\alpha$ for the $\alpha$-fractional derivative. The weights of the approximation scheme have the same rate-matrix type properties as the popular Gr\"unwald scheme. In particular,…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
In this article, a numerical scheme is introduced for solving the fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM) by using an efficient class of finite difference methods. The…
We present a fourth order convergent (2+1) numerical code to solve the Teukolsky equation in the time domain. Our approach is to rewrite the Teukolsky equation as a system of first order differential equations. In this way we get a system…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
Time-fractional telegraph equations provide fundamental mathematical models for transport processes that exhibit memory and nonlocal effects in industrial and physical systems. These models arise naturally in heat transport in materials…