[图书][B] Splitting methods in communication, imaging, science, and engineering
This book is about computational methods based on operator splitting. It consists of twenty-
three chapters written by recognized splitting method contributors and practitioners, and …
three chapters written by recognized splitting method contributors and practitioners, and …
Operator splitting
S MacNamara, G Strang - Splitting methods in communication, imaging …, 2016 - Springer
Operator splitting is a numerical method of computing the solution to a differential equation.
The splitting method separates the original equation into two parts over a time step …
The splitting method separates the original equation into two parts over a time step …
A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance
In this paper, we propose and analyze a positivity-preserving, energy stable numerical
scheme for a certain type of reaction-diffusion systems involving the Law of Mass Action with …
scheme for a certain type of reaction-diffusion systems involving the Law of Mass Action with …
Order estimates in time of splitting methods for the nonlinear Schrödinger equation
In this paper, we consider the nonlinear Schrödinger equation u_t+iΔu-F(u)=0 in two
dimensions. We show, by an operator-theoretic proof, that the well-known Lie and Strang …
dimensions. We show, by an operator-theoretic proof, that the well-known Lie and Strang …
Convergence analysis of the variational operator splitting scheme for a reaction-diffusion system with detailed balance
We present a detailed convergence analysis for an operator splitting scheme proposed in
[C. Liu, C. Wang, and Y. Wang, J. Comput. Phys., 436 (2021), 110253] for a reaction …
[C. Liu, C. Wang, and Y. Wang, J. Comput. Phys., 436 (2021), 110253] for a reaction …
Splitting methods with complex times for parabolic equations
F Castella, P Chartier, S Descombes… - BIT Numerical …, 2009 - Springer
Using composition procedures, we build up high order splitting methods to solve evolution
equations posed in finite or infinite dimensional spaces. Since high-order splitting methods …
equations posed in finite or infinite dimensional spaces. Since high-order splitting methods …
Stability and convergence of Strang splitting. Part I: scalar Allen-Cahn equation
We consider a class of second-order Strang splitting methods for Allen-Cahn equations with
polynomial or logarithmic nonlinearities. For the polynomial case both the linear and the …
polynomial or logarithmic nonlinearities. For the polynomial case both the linear and the …
Some facts about operator-splitting and alternating direction methods
The main goal of this chapter is to give the reader a (relatively) brief overview of operator-
splitting, augmented Lagrangian and ADMM methods and algorithms. Following a general …
splitting, augmented Lagrangian and ADMM methods and algorithms. Following a general …
A second-order accurate, operator splitting scheme for reaction-diffusion systems in an energetic variational formulation
A second-order accurate in time, positivity-preserving, and unconditionally energy stable
operator splitting scheme is proposed and analyzed for reaction-diffusion systems with the …
operator splitting scheme is proposed and analyzed for reaction-diffusion systems with the …
Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: singular perturbation and order reduction
S Descombes, M Massot - Numerische Mathematik, 2004 - Springer
In this paper, we perform the numerical analysis of operator splitting techniques for
nonlinear reaction-diffusion systems with an entropic structure in the presence of fast scales …
nonlinear reaction-diffusion systems with an entropic structure in the presence of fast scales …