Mixed problems for the time-dependent telegraph equation: Continuous numerical solutions with a priori error bounds

  • Authors:

  • P. Almenar;L. Jódar;J. A. Martin

  • Affiliations:

  • Departamento de Matemática Aplicada Universidad Politécnica de Valencia P.O. Box 22012 Valencia, Spain;Departamento de Matemática Aplicada Universidad Politécnica de Valencia P.O. Box 22012 Valencia, Spain;Departamento de Análisis Matemático y Matemática Aplicada Universidad de Alicante P.O. Box 99, E-03080 Alicante, Spain

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 1997

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Abstract

This paper deals with the construction of continuous numerical solutions of mixed problems described by the time-dependent telegraph equation u"t"t + c(t)u"t + b(t)u = a(t)u"x"x, 0 0. Here a(t), b(t), andc(t) are positive functions with appropiate additional alternative hypotheses. First, using the separation of variables technique a theoretical series solution is obtained. Then, after truncation using one-step matrix methods and interpolating functions, a continuous numerical solution with a prefixed accuracy in a bounded subdomain is constructed.