The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
SIAM Journal on Numerical Analysis
Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows
Journal of Computational Physics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
Starting algorithms for IRK methods
Journal of Computational and Applied Mathematics
Stage Value Predictors and Efficient Newton Iterations in Implicit Runge--Kutta Methods
SIAM Journal on Scientific Computing
IRK methods for DAE: starting algorithms
Proceedings of the on Numerical methods for differential equations
Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations
Recent trends in numerical analysis
Starting algorithms for low stage order RKN methods
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Variable-order starting algorithms for implicit Runge-Kutta methods on stiff problems
Applied Numerical Mathematics
Additive Runge-Kutta schemes for convection-diffusion-reaction equations
Applied Numerical Mathematics
Are high order variable step equistage initializers better than standard starting algorithms?
Journal of Computational and Applied Mathematics
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
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Additive and partitioned Runge-Kutta methods are widely used for the numerical integration of some special ODEs. They usually involve the numerical solution of nonlinear systems that require starting values as accurate as possible. In this paper we consider stage value predictors for these kind of methods. First, we deal with partitioned Runge-Kutta methods. The results obtained are transferred to additive Runge-Kutta methods. The theory developed is used to construct starting values for the Lobatto IIIA-IIIB methods and some IMEX methods from the literature. Some numerical results show that the use of the stage value predictors considered in this paper reduces the number of iterations per step and hence the computational cost.