Mixed problems for the time-dependent telegraph equation: Continuous numerical solutions with a priori error bounds |
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Institution: | 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 |
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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 utt + c(t)ut + b(t)u = a(t)uxx, 0 < x < d, t > 0. Here a(t), b(t), and c(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. |
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