Journal of Computational and Applied Mathematics
Diagonally implicit Runge-Kutta-Nystro¨m methods for oscillatory problems
SIAM Journal on Numerical Analysis
VODE: a variable-coefficient ODE solver
SIAM Journal on Scientific and Statistical Computing
Algorithm 670: a Runge-Kutta-Nyström code
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
Iterative schemes for three-stage implicit Runge-Kutta methods
Applied Numerical Mathematics
SDIRK methods for stiff ODEs with oscillating solutions
Journal of Computational and Applied Mathematics
Parallel linear system solvers for Runge-Kutta-Nyström methods
ICCAM '96 Proceedings of the seventh international congress on Computational and applied mathematics
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes
Journal of Computational and Applied Mathematics
Efficient iterations for Gauss methods on second-order problems
Journal of Computational and Applied Mathematics
Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
A code based on the two-stage Gauss formula (order four) for second-order initial value problems of a special type is developed. This code can be used to obtain a low- to medium-precision integration for a wide range of problems in the class of oscillatory type, Hamiltonian problems, and time-dependent partial differential equations discretized in space by finite differences or finite elements. The iteration process used in solving for the stage values of the Gauss formula, the selection of the initial step size, and the choice of an appropriate local error estimator for determining the step size change according to a particular tolerance specified by the user are studied. Moreover, a global error estimate and a dense output at equidistant points in the integration interval are supplied with the code. Numerical experiments and some comparisons with certain standard codes on relevant test problems are also given.