Array-representation integration factor method for high-dimensional systems

DOI10.1016/j.jcp.2013.11.002zbMath1349.65401OpenAlexW2166208892WikidataQ41862832 ScholiaQ41862832MaRDI QIDQ348624

Lei Zhang, Dongyong Wang, Qing Nie

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2013.11.002

zbMATH Keywords

implicit methodFokker-Planck equationsreaction-diffusion equationssplitting methodchemical master equation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items

Fast high-order compact exponential time differencing Runge-Kutta methods for second-order semilinear parabolic equations, Krylov implicit integration factor methods for semilinear fourth-order equations, Semi-implicit integration factor methods on sparse grids for high-dimensional systems, An integration factor method for stochastic and stiff reaction-diffusion systems, Fully discretized energy stable schemes for hydrodynamic equations governing two-phase viscous fluid flows, Fast compact implicit integration factor method with non-uniform meshes for the two-dimensional nonlinear Riesz space-fractional reaction-diffusion equation, Computational complexity study on Krylov integration factor WENO method for high spatial dimension convection-diffusion problems, Efficient Exponential Integrator Finite Element Method for Semilinear Parabolic Equations, A second-order exponential time differencing scheme for non-linear reaction-diffusion systems with dimensional splitting, A compact finite difference method for reaction-diffusion problems using compact integration factor methods in high spatial dimensions, Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations, A fast compact time integrator method for a family of general order semilinear evolution equations, A fast compact exponential time differencing method for semilinear parabolic equations with Neumann boundary conditions, Efficient and Stable Exponential Runge-Kutta Methods for Parabolic Equations, A conservative numerical method for the fractional nonlinear Schrödinger equation in two dimensions, Krylov integration factor method on sparse grids for high spatial dimension convection-diffusion equations, Fast explicit integration factor methods for semilinear parabolic equations

Cites Work

• Unnamed Item
• Krylov implicit integration factor methods for spatial discretization on high-dimensional unstructured meshes: application to discontinuous Galerkin methods
• Operator splitting implicit integration factor methods for stiff reaction-diffusion-advection systems
• Exponential time differencing for stiff systems
• Generalized integrating factor methods for stiff PDEs
• Solving the chemical master equation for monomolecular reaction systems analytically
• Compact integration factor methods in high spatial dimensions
• Compact integration factor methods for complex domains and adaptive mesh refinement
• A new class of time discretization schemes for the solution of nonlinear PDEs
• Weighted essentially non-oscillatory schemes
• Removing the stiffness from interfacial flows with surface tension
• The Fokker-Planck equation. Methods of solutions and applications.
• Efficient implementation of weighted ENO schemes
• Efficient semi-implicit schemes for stiff systems
• An ETD Crank-Nicolson method for reaction-diffusion systems
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• Efficient Solution of Parabolic Equations by Krylov Approximation Methods
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Fourth-Order Time-Stepping for Stiff PDEs
• On the Construction and Comparison of Difference Schemes
• Fokker–Planck approximation of the master equation in molecular biology