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. .
Ann. Phys
J. Vib. Control
PhysicaD
Signal Process
Phys. A
J. Vib. Control
Ann. Phys
116
Appl. Math. Comput
NonlinearDyn
Appl. Math. Comput
Physica A: Statistical Mechanics and its Applications
Nonlinear Dyn
Appl. Math. Lett
SIAM J. Sci. Comput
Appl. Numer. Math
Comput. Math. Appl
Comput. Math. Appl
J. Comput. Phys
J. Comput. Phys
117 ...
Appl. Math. Lett
Appl. Math. Lett
J. Comput. Phys
Appl. Math. Comput
Appl. Math. Comput
Appl. Math. Comput
Appl. Math. Model
J.Comput. Appl. Math
Numer. Algor
Eur. Phys. J. Plus
J. Appl. Math. Comput
Comput. Math. Appl
118
J. Comput. Appl. Math
J. Comput. Phys
Commun. Nonlinear. Sci. Numer. Simulat
119 ...
Keywords: