Two-step fourth-order P-stable methods with phase-lag of order six for y″=(t,y)
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Phase-lag analysis of implicit Runge-Kutta methods
SIAM Journal on Numerical Analysis
Diagonally implicit Runge-Kutta-Nystro¨m methods for oscillatory problems
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
SDIRK methods for stiff ODEs with oscillating solutions
Journal of Computational and Applied Mathematics
Efficient iterations for Gauss methods on second-order problems
Journal of Computational and Applied Mathematics
Stability of Runge-Kutta-Nyström methods
Journal of Computational and Applied Mathematics
Mathematical and Computer Modelling: An International Journal
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A general analysis of accuracy and linear stability of Runge-Kutta-Nystrom (RKN) methods for solving second-order stiff problems is carried out. This analysis reveals that when components with large frequencies (stiff frequencies) and small amplitudes appear in the solution of the problem, the accuracy of an unconditionally stable RKN method can be seriously affected unless certain algebraic conditions are satisfied. Based on these algebraic conditions we derive new fourth-order A-stable diagonally implicit RKN (DIRKN) methods with different dispersion order and stage order. The numerical experiments carried out show the efficiency of the new methods when they are compared with other DIRKN codes proposed in the scientific literature for solving second-order stiff problems.