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
Triangularly Implicit Iteration Methods for ODE-IVP Solvers
SIAM Journal on Scientific Computing
A note on the efficient implementation of implicit methods for ODEs
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
Blended block BVMs (B3VMs): a family of economical implicit methods for ODEs
Journal of Computational and Applied Mathematics
Blended Linear Multistep Methods
ACM Transactions on Mathematical Software (TOMS)
Block implicit methods for Odes
Recent trends in numerical analysis
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)
Economical error estimates for block implicit methods for ODEs via deferred correction
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Recent advances in linear analysis of convergence for splittings for solving ODE problems
Applied Numerical Mathematics
On the relations between B2V Ms and Runge-Kutta collocation methods
Journal of Computational and Applied Mathematics
Economical error estimates for block implicit methods for ODEs via deferred correction
Applied Numerical Mathematics
Blended implicit methods for the numerical solution of DAE problems
Journal of Computational and Applied Mathematics
A note on the efficient implementation of Hamiltonian BVMs
Journal of Computational and Applied Mathematics
An Error Corrected Euler Method for Solving Stiff Problems Based on Chebyshev Collocation
SIAM Journal on Numerical Analysis
Efficient implementation of Gauss collocation and Hamiltonian boundary value methods
Numerical Algorithms
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In this paper we further develop a new approach for naturally defining the nonlinear splittings needed for the implementation of block implicit methods for ODEs, which has been considered by Brugnano [J. Comput. Appl. Math. 116 (2000) 41] and by Brugnano and Trigiante [in: Recent Trends in Numerical Analysis, Nova Science, New York, 2000, pp. 81-105]. The basic idea is that of defining the numerical method as the combination (blending) of two suitable component methods. By carefully choosing such methods, it is shown that very efficient implementations can be obtained. Moreover, some of them, characterized by a diagonal splitting, are well suited for parallel computers. Some numerical tests comparing the performances of the proposed implementation with other existing ones are also presented, in order to make evident the potential of the approach.