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Manuscript Title: Some procedures for the construction of high-order exponentially fitted Runge-Kutta-Nyström methods of explicit type
Authors: J.M. Franco, I. Gómez
Program title: SVI-IIEXPOreferee.for and SVI-IIvarreferee.for
Catalogue identifier: AEOO_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 184(2013)1310
Programming language: Fortran 77.
Computer: Standard PC.
Operating system: Windows. It might work with others. Successfully tested by CPC on Linux.
RAM: For the test problems used less than 1 MB.
Keywords: Exponential fitting, Runge-Kutta-Nyström methods, Symmetric and symplectic methods, Parallel methods, Oscillatory differential systems.
Classification: 4.3, 4.12, 16.3, 17.17.

Nature of problem:
Some models in astronomy and astrophysics, quantum mechanics and nuclear physics lead to second-order oscillatory differential systems. The solution of these oscillatory models requires accurate and efficient numerical methods. The codes SVI-IIEXPOreferee.for and SVI-IIvarreferee.for were developed for this purpose.

Solution method:
We propose high-order exponentially fitted Runge-Kutta-Nyström (EFRKN) methods of explicit type for solving second-order oscillatory models. The code SVI-IIEXPOreferee.for contains symmetric and symplectic EFRKN methods with orders six and eight, and it runs with fixed step. The variable-step code SVI-IIvarreferee.for contains embedded pairs of EFRKN methods with orders 8(6), 10(8) and 12(10).

The codes are designed for solving second-order oscillatory differential systems with 200 equations. If the number of differential equations is greater than 200, then the dimension must be increased in the program.

Additional comments:
The codes require the fitting frequency of the problem.

Running time:
The test problems used require only a few seconds to run.