相关论文: An initial-corrected splitting approach for convec…

We present modifications of the second-order Douglas stabilizing corrections method, which is a splitting method based on the implicit trapezoidal rule. Inclusion of an explicit term in a forward Euler way is straightforward, but this will…

A second-order accurate in time, positivity-preserving, and unconditionally energy stable operator splitting numerical scheme is proposed and analyzed for the system of reaction-diffusion equations with detailed balance. The scheme is…

In this work, we show high order splitting methods of integration without negative steps, allowing us to solve numerically irreversible problems, like reaction-diffusion equations. The methods consist in a suitable affine combinations 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…

We present a new discretization for advection-diffusion problems with Robin boundary conditions on complex time-dependent domains. The method is based on second order cut cell finite volume methods introduced by Bochkov et al. to discretize…

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…

This paper develops a two-level fourth-order scheme for solving time-fractional convection-diffusion-reaction equation with variable coefficients subjected to suitable initial and boundary conditions. The basis properties of the new…

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…

This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…

In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…

We present a detailed convergence analysis for an operator splitting scheme proposed in [C. Liu et al.,J. Comput. Phys., 436, 110253, 2021] for a reaction-diffusion system with detailed balance. The numerical scheme has been constructed…

This paper studies adaptive least-squares finite element methods for convection-dominated diffusion-reaction problems. The least-squares methods are based on the first-order system of the primal and dual variables with various ways of…

For astrophysical reacting flows, operator splitting is commonly used to couple hydrodynamics and reactions. Each process operates independent of one another, but by staggering the updates in a symmetric fashion (via Strang splitting)…

A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…

We use the perturbation method to approximately solve subdiffusion-reaction equations. Within this method we obtain the solutions of the zeroth and the first order. The comparison our analytical solutions with the numerical results shown…

In this paper, a new fractional step method is proposed for simulating stiff and nonstiff chemically reacting flows. In stiff cases, a well-known spurious numerical phenomenon, i.e. the incorrect propagation speed of discontinuities, may be…

In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…

We provide the proof of convergence of the directional diffusion splitting scheme for two-dimensional parabolic and elliptic advection-diffusion-reaction problems with certain restrictions on problem data

In this paper a technique is given to recover the classical order of the method when explicit exponential Runge-Kutta methods integrate reaction-diffusion problems. Although methods of high stiff order for problems with vanishing boundary…

A fourth-order compact scheme is proposed for a fourth-order subdiffusion equation with the first Dirichlet boundary conditions. The fourth-order problem is firstly reduced into a couple of spatially second-order system and we use an…