Two FORTRAN packages for assessing initial value methods
ACM Transactions on Mathematical Software (TOMS)
Stiff ode slovers: a review of current and coming attractions
Journal of Computational Physics
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Towards efficient Runge-Kutta methods for stiff systems
SIAM Journal on Numerical Analysis
A Transformed implicit Runge-Kutta Method
Journal of the ACM (JACM)
A class of multistep methods based on a super-future points technique for solving IVPs
Computers & Mathematics with Applications
Class 2+1 Hybrid BDF-Like methods for the numerical solutions of ordinary differential equations
Calcolo: a quarterly on numerical analysis and theory of computation
| Hi-index | 0.00 |
In a recent publication Butcher and Cash introduced a new class of L-stable implicit Runge-Kutta formulae in an attempt to eliminate the disadvantages of SIRK and DIRK formulae and to combine their advantages. These formulae, namely Diagonally Extended Singly Implicit formulae (DESI), have been investigated by the present author and have been implemented in an experimental code in a variable-stepsize/variable-order mode. Numerical experimentation on a large number of stiff systems has shown that the DESI code is much more efficient than STRIDE (which is an implementation of SIRK formulae) and competitive with BDF implementations. In this paper we investigate the efficiency of the DESI code on large dimension stiff systems with banded Jacobians, which arise from the discretization of PDEs with the Numerical Method of Lines (NUMOL). The results obtained by the DESI code are compared with the results obtained by the widely used BDF code LSODE. These results indicate that the current implementation of DESI performs satisfactorily and, in particular, is competitive with LSODE.