The exponential accuracy of Fourier and Chebyshev differencing methods
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
Exponential time differencing for stiff systems
Journal of Computational Physics
Symmetric multistep methods over long times
Numerische Mathematik
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
SIAM Journal on Numerical Analysis
Exponential Runge--Kutta methods for parabolic problems
Applied Numerical Mathematics
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In this paper, a general procedure is given to construct explicit high-order symmetric multistep cosine methods. For these integrators, stability for stiff problems and order of consistency under hypotheses of regularity are justified. We also study when resonances can turn up for the methods suggested and give a simple technique to filter them without losing order of consistency. Particular methods of order eight and ten are explicitly constructed and their high efficiency is numerically shown when integrating Euler-Bernoulli equation.