相关论文: Weighted average finite difference methods for fra…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
The Nitsche method is a method of "weak imposition" of the inhomogeneous Dirichlet boundary conditions for partial differential equations. This paper explains stability and convergence study of the Nitsche method applied to evolutionary…
Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases…
This work studies exact solvability of a class of fractional reaction-diffusion equation with the Riemann-Liouville fractional derivatives on the half-line in terms of the similarity solutions. We derived the conditions for the equation to…
In this paper we present a difference algebraic technique for the evaluation of the Einstein's strength of a system of partial difference equations and apply this technique to the comparative analysis of difference schemes for chemical…
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
The existence and stability results for a class of fractional differential equations involving generalized Katugampola derivative are presented herein. Some fixed point theorems are used and enlightening examples of obtained result are also…
A discretization scheme is introduced for a set of convection-diffusion equations with a non-linear reaction term, where the convection velocity is constant for each reactant. This constancy allows a transformation to new spatial variables,…
In this paper, we consider mixed finite element semi-/full discretizations of the Rosensweig ferrofluid flow model. We first establish some regularity results for the model under several basic assumptions. Then we show that the energy…
In this paper, a class of finite difference numerical techniques is presented to solve the second-order linear inhomogeneous damped wave equation. The consistency, stability, and convergences of these numerical schemes are discussed. The…
The paper introduces a finite element method for an Eulerian formulation of partial differential equations governing the transport and diffusion of a scalar quantity in a time-dependent domain. The method follows the idea from Lehrenfeld &…
We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity…
We develop mixed finite element methods for nonlinear reaction-diffusion equations with interfaces which have Robin-type interface conditions. We introduce the velocity of chemicals as new variables and reformulate the governing equations.…
Fractional diffusion equations for three-dimensional lattice models based on fractional-order differences of the Grunwald-Letnikov type are suggested. These lattice fractional diffusion equations contain difference operators that describe…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Fractional variational approach has gained much attention in recent years. There are famous fractional derivatives such as Caputo derivative, Riesz derivative and Riemann-Liouville derivative. Several versions of fractional variational…
In this paper, we consider a fast and second-order implicit difference method for approximation of a class of time-space fractional variable coefficients advection-diffusion equation. To begin with, we construct an implicit difference…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…