Dissipative Chebyshev exponential-fitted methods for numerical solution of second-order differential equations

  • Authors:

  • Jesús Vigo-Aguiar;Higinio Ramos

  • Affiliations:

  • Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Salamanca, Salamanca 37008, Spain;Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Salamanca, Salamanca 37008, Spain and Escuela Politécnica Superior, Campus Viriato, Zamora, Spain

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Selected papers from the conference on computational and mathematical methods for science and engineering (CMMSE-2002) Alicante University, Spain, 20-25 september 2002
  • Year:
  • 2003

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Abstract

A family of implicit methods based on intra-step Chebyshev interpolation has been developed to integrate oscillatory second-order initial value problems of the form y"(t)- 2g y'(t)+ (g2+ w2)y(t)= f(t,y(t)). The procedure integrates the homogeneous part exactly (in the absence of round-off errors). The Chebyshev approach uses stepsizes that are considerably larger than those typically used in Runge-Kutta or multistep methods. Computational overheads are comparable to those incurred by high-order conventional procedures. Chebyshev interpolation coupled with the exponential-fitted nature of the method substantially reduces local errors. Global error propagation rates are also reduced making these procedures good candidates to be used in long-term simulations of perturbed oscillatory systems with a dissipative term.