Two classes of implicit-explicit multistep methods for nonlinear stiff initial-value problems

DOI10.1016/j.amc.2014.08.066zbMath1338.65179OpenAlexW1977379644MaRDI QIDQ297677

Gengen Zhang, Xing Yi, Ai-Guo Xiao

Publication date: 17 June 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.08.066

zbMATH Keywords

convergencelinear multistep methodsstiff problemsone-leg methodsimplicit-explicit multistep methodssingular perturbation problems

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for stiff equations (65L04)

Related Items

New algorithm for first order stiff initial value problems ⋮ Implicit-Explicit Runge-Kutta-Rosenbrock Methods with Error Analysis for Nonlinear Stiff Differential Equations ⋮ Numerical approximation to semi-linear stiff neutral equations via implicit-explicit general linear methods ⋮ Stability and convergence analysis of implicit–explicit one-leg methods for stiff delay differential equations ⋮ Model reduction and implicit-explicit Runge-Kutta schemes for nonlinear stiff initial-value problems ⋮ A stiff-cut splitting technique for stiff semi-linear systems of differential equations ⋮ A two-level linearized compact ADI scheme for two-dimensional nonlinear reaction-diffusion equations ⋮ Implicit-explicit time discretization coupled with finite element methods for delayed predator-prey competition reaction-diffusion system ⋮ Stability analysis of implicit-explicit \(\theta\)-methods for composite stiff neutral functional differential equations in Banach space ⋮ Implicit-explicit one-leg methods for nonlinear stiff neutral equations ⋮ Implicit–explicit multistep finite-element methods for nonlinear convection-diffusion-reaction equations with time delay

Uses Software

• IRKC

Cites Work

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• Total-variation-diminishing implicit-explicit Runge-Kutta methods for the simulation of double-diffusive convection in astrophysics
• Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation
• Relaxation method for unsteady convection-diffusion equations
• Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
• Implicit-explicit predictor-corrector schemes for nonlinear parabolic differential equations
• Stability of two IMEX methods, CNLF and BDF2-AB2, for uncoupling systems of evolution equations
• Modern convergence theory for stiff initial-value problems
• Convergence of linear multistep and one-leg methods for stiff nonlinear initial value problems
• On the convergence of multistep methods for nonlinear stiff differential equations
• Some new additive Runge-Kutta methods and their applications
• On an accurate third order implicit-explicit Runge-Kutta method for stiff problems
• Stability of implicit-explicit linear multistep methods for ordinary and delay differential equations
• On the equivalence of \(A\)-stability and \(G\)-stability
• Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
• On the stability of implicit-explicit linear multistep methods
• On the contractivity of implicit-explicit linear multistep methods
• Implicit-explicit multistep methods for quasilinear parabolic equations
• Additive Runge-Kutta schemes for convection-diffusion-reaction equations
• Implicit-explicit BDF methods for the Kuramoto-Sivashinsky equation
• An implicit-explicit approach for atmospheric transport-chemistry problems
• Entropy stable numerical schemes for two-fluid plasma equations
• Implicit-explicit methods based on strong stability preserving multistep time discretizations
• Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
• IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
• IMEX Runge-Kutta schemes for reaction-diffusion equations
• IRKC: an IMEX solver for stiff diffusion-reaction PDEs
• G-stability is equivalent toA-stability
• 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
• An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Implicit–explicit multistep methods for nonlinear parabolic equations
• Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit
• Strong Stability for Additive Runge–Kutta Methods