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
Parallel predictor-corrector methods
Proceedings of the 6th international congress on Computational and applied mathematics
CWI contributions to the development of parallel Runge-Kutta methods
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
On the diagonal approximation of full matrices
Journal of Computational and Applied Mathematics
Triangularly Implicit Iteration Methods for ODE-IVP Solvers
SIAM Journal on Scientific Computing
Parallel linear system solvers for Runge-Kutta-Nyström methods
ICCAM '96 Proceedings of the seventh international congress on Computational and applied mathematics
A note on the efficient implementation of implicit methods for ODEs
Journal of Computational and Applied Mathematics
On the generation of mono-implicit Runge-Kutta-Nystro¨m methods by mono-implicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Analysis of approximate factorization in iteration methods
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Blended block BVMs (B3VMs): a family of economical implicit methods for ODEs
Journal of Computational and Applied Mathematics
Block implicit methods for Odes
Recent trends in numerical analysis
Blended implementation of block implicit methods for ODEs
Applied Numerical Mathematics
The BiM code for the numerical solution of ODEs
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Journal of Computational and Applied Mathematics
Efficient iterations for Gauss methods on second-order problems
Journal of Computational and Applied Mathematics
Blended implicit methods for the numerical solution of DAE problems
Journal of Computational and Applied Mathematics
On the relations between B2V Ms and Runge-Kutta collocation methods
Journal of Computational and Applied Mathematics
A note on the efficient implementation of Hamiltonian BVMs
Journal of Computational and Applied Mathematics
Efficient implementation of Gauss collocation and Hamiltonian boundary value methods
Numerical Algorithms
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In the nineties, Van der Houwen et al. (see, e.g., [P.J. van der Houwen, B.P. Sommeijer, J.J. de Swart, Parallel predictor-corrector methods, J. Comput. Appl. Math. 66 (1996) 53-71; P.J. van der Houwen, J.J.B. de Swart, Triangularly implicit iteration methods for ODE-IVP solvers, SIAM J. Sci. Comput. 18 (1997) 41-55; P.J. van der Houwen, J.J.B. de Swart, Parallel linear system solvers for Runge-Kutta methods, Adv. Comput. Math. 7 (1-2) (1997) 157-181]) introduced a linear analysis of convergence for studying the properties of the iterative solution of the discrete problems generated by implicit methods for ODEs. This linear convergence analysis is here recalled and completed, in order to provide a useful quantitative tool for the analysis of splittings for solving such discrete problems. Indeed, this tool, in its complete form, has been actively used when developing the computational codes BiM and BiMD [L. Brugnano, C. Magherini, The BiM code for the numerical solution of ODEs, J. Comput. Appl. Math. 164-165 (2004) 145-158. Code available at: http://www.math.unifi.it/~brugnano/BiM/index.html; L. Brugnano, C. Magherini, F. Mugnai, Blended implicit methods for the numerical solution of DAE problems, J. Comput. Appl. Math. 189 (2006) 34-50]. Moreover, the framework is extended for the case of special second order problems. Examples of application, aimed to compare different iterative procedures, are also presented.