Related papers: Overcoming order reduction in diffusion-reaction s…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
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,…
In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second-order accurate convex splitting scheme for the Modified Phase Field Crystal equation, a generalized damped wave equation for which the…
We carry out the enhanced group classification of a class of (1+1)-dimensional nonlinear diffusion-reaction equations with gradient-dependent diffusivity using the two-step version of the method of furcate splitting. For simultaneously…
One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
In this paper, we focus on designing a well-conditioned Glarkin spectral methods for solving a two-sided fractional diffusion equations with drift, in which the fractional operators are defined neither in Riemann-Liouville nor Caputo sense,…
We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
We propose a quasi-random operator splitting method for evolution equations driven by multiple mechanisms. The method uses a low-discrepancy sequence to generate the ordering of the subflows, while requiring only one application of each…
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…
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…
In a retroreflective scheme atomic Raman diffraction adopts some of the properties of Bragg diffraction due to additional couplings to off-resonant momenta. As a consequence, double Raman diffraction has to be performed in a Bragg-type…
We consider quadrature formulas of high order in time based on Radau-type, L-stable implicit Runge-Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
In this paper, we propose a novel numerical scheme for solving time-fractional reaction-diffusion problems with Robin boundary conditions, where the time derivative is in the Caputo sense of order $\alpha\in(0,1)$. The existence and…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
The Strang splitting method has been widely used to solve nonlinear reaction-diffusion equations, with most theoretical convergence analysis assuming periodic boundary conditions. However, such analysis presents additional challenges for…