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
Explicit Runge-Kutta methods for parabolic partial differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Runge-Kutta-Nystro¨m methods for general second order ODEs with application to multi-body systems
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Nyström methods and singular second-order differential equations
Computers & Mathematics with Applications
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Structural dynamics applications feature a particular type of second order stiff equations, often in combination with low smoothness of the right side, large dimension and non-linear forcing terms. As alternative to implicit schemes, explicit Runge-Kutta-Nyström methods are analysed, with focus on low order and maximized stability domain since spurious high frequency oscillations need not be resolved. It turns out that it is possible to construct methods with a stability domain that stretches up to hω = 2s on the imaginary axis where h is the stepsize, ω the largest frequency in the system, and s the stage number. Simulation examples generated by FEMLAB show that the methods are competitive.