New methods for oscillatory problems based on classical codes

Authors:
Amelia García;Pablo Martí;Ana B. González
Affiliations:
Departamento de Matemática Aplicada a la Ingeniería, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, Paseo del Caucs s/n, 47011 Valladolid, Spain;Departamento de Matemática Aplicada a la Ingeniería, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, Paseo del Caucs s/n, 47011 Valladolid, Spain;Departamento de Matemática Aplicada a la Ingeniería, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, Paseo del Caucs s/n, 47011 Valladolid, Spain
Venue:
Applied Numerical Mathematics
Year:
2002

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Abstract

The numerical integration of differential equations with oscillatory solutions is a very common problem in many fields of the applied sciences. Some methods have been specially devised for this kind of problem. In most of them, the calculation of the coefficients needs more computational effort than the classical codes because such coefficients depend on the step-size in a not simple manner. On the contrary, in this work we present new algorithms specially designed for perturbed oscillators whose coefficients have a simple dependence on the step-size. The methods obtained are competitive when comparing with classical and special codes.