Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs

Linearly Implicit and High-Order Energy-Conserving Schemes for Nonlinear Wave Equations

(2020) Dongfang Li et al.   JOURNAL OF SCIENTIFIC COMPUTING

Relaxation Runge–Kutta Methods for Hamiltonian Problems

(2020) Hendrik Ranocha et al.   JOURNAL OF SCIENTIFIC COMPUTING

Higher-order additive Runge–Kutta schemes for ordinary differential equations

(2018) Christopher A. Kennedy et al.   APPLIED NUMERICAL MATHEMATICS

Maximum norm analysis of implicit–explicit backward difference formulae for nonlinear parabolic equations

(2017) Georgios Akrivis et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

New conservative difference schemes with fourth-order accuracy for some model equation for nonlinear dispersive waves

(2017) Ahlem Ghiloufi et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

A Unified IMEX Runge--Kutta Approach for Hyperbolic Systems with Multiscale Relaxation

(2017) Sebastiano Boscarino et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Construction of high-order Runge–Kutta methods which preserve delay-dependent stability of DDEs

(2016) Dongfang Li et al.   APPLIED MATHEMATICS AND COMPUTATION

Numerical methods for non conservative perturbations of conservative problems

(2015) M.P. Laburta et al.   COMPUTER PHYSICS COMMUNICATIONS

Linearly Implicit IMEX Runge--Kutta Methods for a Class of Degenerate Convection-Diffusion Problems

(2015) Sebastiano Boscarino et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Optimized strong stability preserving IMEX Runge–Kutta methods

(2014) Inmaculada Higueras et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems

(2014) Luigi Brugnano et al.   NUMERICAL ALGORITHMS

Flux-Explicit IMEX Runge--Kutta Schemes for Hyperbolic to Parabolic Relaxation Problems

(2013) Sebastiano Boscarino et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit

(2013) S. Boscarino et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Implicit–explicit multistep methods for nonlinear parabolic equations

(2012) Georgios Akrivis   MATHEMATICS OF COMPUTATION

Energy- and Quadratic Invariants--Preserving Integrators Based upon Gauss Collocation Formulae

(2012) Luigi Brugnano et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

On stability issues for IMEX schemes applied to 1D scalar hyperbolic equations with stiff reaction terms

(2011) R. Donat et al.   MATHEMATICS OF COMPUTATION

Projection methods preserving Lyapunov functions

(2010) M. Calvo et al.   BIT NUMERICAL MATHEMATICS

On a Class of Uniformly Accurate IMEX Runge–Kutta Schemes and Applications to Hyperbolic Systems with Relaxation

(2009) Sebastiano Boscarino et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

On an accurate third order implicit-explicit Runge–Kutta method for stiff problems

(2008) Sebastiano Boscarino   APPLIED NUMERICAL MATHEMATICS

IMEX Runge–Kutta schemes for reaction–diffusion equations

(2007) Toshiyuki Koto   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS