Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
An implicit-explicit approach for atmospheric transport-chemistry problems
Applied Numerical Mathematics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
On the stability of implicit-explicit linear multistep methods
Applied Numerical Mathematics - Special issue on time integration
Linearly implicit Runge—Kutta methods for advection—reaction—diffusion equations
Applied Numerical Mathematics
Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations
Recent trends in numerical analysis
Central Schemes for Balance Laws of Relaxation Type
SIAM Journal on Numerical Analysis
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
Implicit-explicit time stepping with spatial discontinuous finite elements
Applied Numerical Mathematics
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
Contractivity/monotonicity for additive Runge-Kutta methods: inner product norms
Applied Numerical Mathematics
Error Analysis of IMEX Runge-Kutta Methods Derived from Differential-Algebraic Systems
SIAM Journal on Numerical Analysis
Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation
Journal of Computational Physics
High accuracy solutions to energy gradient flows from material science models
Journal of Computational Physics
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Most of the popular implicit-explicit (IMEX) Runge-Kutta (R-K) methods existing in the literature suffer from the phenomenon of order reduction in the stiff regime when applied to stiff problems containing a non-stiff term and a stiff term. Specifically, order reduction is observed when the problem becomes increasingly stiff. In this paper, our motivation is to derive a third-order IMEX R-K method for stiff problems that has a better temporal order of convergence than other well-known IMEX R-K methods. A comparison with other third-order methods shows substantial potential of this new method.