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
An MEBDF code for stiff initial value problems
ACM Transactions on Mathematical Software (TOMS)
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
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)
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
Recent advances in linear analysis of convergence for splittings for solving ODE problems
Applied Numerical Mathematics
A note on the efficient implementation of Hamiltonian BVMs
Journal of Computational and Applied Mathematics
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The use of implicit numerical methods is mandatory when solving general stiff ODE/DAE problems. Their use, in turn, requires the solution of a corresponding discrete problem, which is one of the main concerns in the actual implementation of the methods. In this respect, blended implicit methods provide a general framework for the efficient solution of the discrete problems generated by block implicit methods. In this paper, we review the main facts concerning blended implicit methods for the numerical solution of ODE and DAE problems. In addition to this, we study the extension of blended implicit methods for solving second-order problems, which results in a straightforward generalization of the basic theory for such methods. Finally, a few numerical tests obtained with the computational code BiMD, implementing a variable order-variable stepsize blended implicit method, are also reported, in order to confirm the effectiveness of the approach.