The Open Applied Mathematics Journal

2007, 1 : 9-14
Published online 2007 August 02. DOI: 10.2174/1874114200701010009
Publisher ID: TOAMJ-1-9

Integration of Highly Oscillatory Problems Through G-Functions

F. García-Alonso , J.A. Reyes and Y. Villacampa
Departamento de Matemática Aplicada, Escuela Politécnica Superior, Universidad de Alicante, Spain.

ABSTRACT

Perturbed harmonic oscillators describe many models in physics and engineering. A method for solving this type of problem is based on the utilization of Scheifele’s functions, consisting of a refinement of the Taylor series method. One disadvantage of the method is that it is difficult to determine, in each case, the recurrence relations necessary for arriving to the solutions. In this paper we construct the numerical method especially adapted to the integration of oscillators, using developments in the form of G-functions. In addition, two computer applications related to highly oscillatory problems are implemented, and recurrence relations are determined in each one. The results show better precision in the application of G-functions, compared to other known methods implemented in MAPLE V.

Keywords:

Numerical solutions of ODE’s, Highly accurate solutions, Highly oscillatory problems.