Asymptotic preserving methods for quasilinear hyperbolic systems with stiff relaxation: a review

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Hyperbolic balance laws with relaxation
Numerical schemes for kinetic equations in diffusive regimes
High order semi-implicit schemes for time dependent partial differential equations
Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
Numerical solutions of partial differential equations
On an accurate third order implicit-explicit Runge-Kutta method for stiff problems
Hyperbolic conservation laws with relaxation
Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
Order conditions for numerical methods for partitioned ordinary differential equations
The Boltzmann equation and its applications
Numerical hydrodynamics from gas-kinetic theory
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
All Mach number second order semi-implicit scheme for the Euler equations of gas dynamics
Higher-order additive Runge-Kutta schemes for ordinary differential equations
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
High order semi-implicit multistep methods for time-dependent partial differential equations
Implicit and semi-implicit well-balanced finite-volume methods for systems of balance laws
High order pressure-based semi-implicit IMEX schemes for the 3D Navier-Stokes equations at all Mach numbers
A high order semi-implicit IMEX WENO scheme for the all-Mach isentropic Euler system
Well-balanced high-order finite volume methods for systems of balance laws
3D simulations of early blood vessel formation
On the asymptotic properties of IMEX Runge-Kutta schemes for hyperbolic balance laws
From hyperbolic systems to kinetic theory. A personalized quest
Central Schemes for Balance Laws of Relaxation Type
Central schemes for hydrodynamical limits of discrete-velocity kinetic models
Scaling limits for the Ruijgrok-Wu model of the Boltzmann equation
Asymptotic Preserving Implicit-Explicit Runge--Kutta Methods for Nonlinear Kinetic Equations
High-Order Asymptotic-Preserving Methods for Fully Nonlinear Relaxation Problems
Discontinuous Galerkin Approximation of Relaxation Models for Linear and Nonlinear Diffusion Equations
Additive Runge-Kutta Methods for Stiff Ordinary Differential Equations
Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation
Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation II. Higher-Order Godunov Methods
Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models
Boltzmann Type Schemes for Gas Dynamics and the Entropy Property
Split Runge-Kutta method for simultaneous equations
Error Analysis of IMEX Runge–Kutta Methods Derived from Differential-Algebraic Systems
On a Class of Uniformly Accurate IMEX Runge–Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Total-Variation-Diminishing Time Discretizations
The fluid-dynamical limit of a nonlinear model boltzmann equation
Additive Methods for the Numerical Solution of Ordinary Differential Equations
A Partially Implicit Method for Large Stiff Systems of ODE<scp>s</scp> with Only Few Equations Introducing Small Time-Constants
Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
Characteristic‐based schemes for dispersive waves I. The method of characteristics for smooth solutions
Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
Hyperbolic conservation laws with stiff relaxation terms and entropy
Relaxation Schemes for Nonlinear Kinetic Equations
An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit
Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems
Extended Hydrodynamical Model of Carrier Transport in Semiconductors
Numerical Schemes for Hyperbolic Systems of Conservation Laws with Stiff Diffusive Relaxation
Central Differencing Based Numerical Schemes for Hyperbolic Conservation Laws with Relaxation Terms
Finite Volume Methods for Hyperbolic Problems
Numerical methods for kinetic equations
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
The relaxation schemes for systems of conservation laws in arbitrary space dimensions
Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit
Flux-Explicit IMEX Runge--Kutta Schemes for Hyperbolic to Parabolic Relaxation Problems
Resurrection of "Second Order" Models of Traffic Flow
Implicit-Explicit Multistep Methods for Hyperbolic Systems With Multiscale Relaxation
On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations
Classical and Relativistic Rational Extended Thermodynamics of Gases
A Weakly Asymptotic Preserving Low Mach Number Scheme for the Euler Equations of Gas Dynamics
Implicit-Explicit Linear Multistep Methods for Stiff Kinetic Equations
A Unified IMEX Runge--Kutta Approach for Hyperbolic Systems with Multiscale Relaxation
Geometric Numerical Integration
Hyperbolic limit of the Jin‐Xin relaxation model
Shock Structure in a Simple Discrete Velocity Gas
Numerical Passage from Kinetic to Fluid Equations
ON DIFFUSION BY DISCONTINUOUS MOVEMENTS, AND ON THE TELEGRAPH EQUATION
Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations

This page was built for publication: Asymptotic preserving methods for quasilinear hyperbolic systems with stiff relaxation: a review