A Second-Order Asymptotic-Preserving and Positivity-Preserving Exponential Runge--Kutta Method for a Class of Stiff Kinetic Equations

DOI10.1137/18M1226774zbMath1435.82023arXiv1807.03728OpenAlexW2858994221WikidataQ115525583 ScholiaQ115525583MaRDI QIDQ5222104

Jingwei Hu, Ruiwen Shu

Publication date: 31 March 2020

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.03728

zbMATH Keywords

positivity-preservingasymptotic-preservingexponential Runge-Kutta methodstiff kinetic equationentropy-decay

Mathematics Subject Classification ID

Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Positive solutions to PDEs (35B09) Numerical methods for stiff equations (65L04) Euler equations (35Q31) Boltzmann equations (35Q20) Fokker-Planck equations (35Q84) Numerical computation of matrix exponential and similar matrix functions (65F60) Finite difference methods applied to problems in statistical mechanics (82M20)

Related Items (7)

Asymptotic-preserving schemes for multiscale physical problems ⋮ A Structure Preserving Numerical Scheme for Fokker--Planck Equations of Structured Neural Networks with Learning Rules ⋮ Accuracy and Stability Analysis of the Semi-Lagrangian Method for Stiff Hyperbolic Relaxation Systems and Kinetic BGK Model ⋮ Spatial second-order positive and asymptotic preserving unified gas kinetic schemes for radiative transfer equations ⋮ High-order exponential integrators for the Riesz space-fractional telegraph equation ⋮ High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge--Kutta Methods with Asymptotic Preserving Properties ⋮ A third-order unconditionally positivity-preserving scheme for production-destruction equations with applications to non-equilibrium flows

Cites Work

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• Exponential Runge-Kutta for the inhomogeneous Boltzmann equations with high order of accuracy
• A class of asymptotic-preserving schemes for the Fokker-Planck-Landau equation
• On maximum-principle-satisfying high order schemes for scalar conservation laws
• The Boltzmann equation and its applications
• Fisher information estimates for Boltzmann's collision operator
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
• Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms
• Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
• Strong Stability-Preserving High-Order Time Discretization Methods
• Time Relaxed Monte Carlo Methods for the Boltzmann Equation
• Exponential integrators
• Asymptotic-Preserving Schemes for Multiscale Hyperbolic and Kinetic Equations
• Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
• Exponential Runge–Kutta Methods for Stiff Kinetic Equations
• Relaxation Schemes for Nonlinear Kinetic Equations
• Asymptotic-Preserving and Positivity-Preserving Implicit-Explicit Schemes for the Stiff BGK Equation
• An Entropic Fourier Method for the Boltzmann Equation
• Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
• Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation
• A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
• The Gaussian-BGK model of Boltzmann equation with small Prandtl number

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