Solución numérica de problemas de valores en la frontera con alta exactitud por métodos espectrales

Camacho-Galván, A.; Guardián-Soto, B.; Rodríguez-Green, M.; Camacho-Galván, A.; Guardián-Soto, B.; Rodríguez-Green, M.

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Ingeniería, investigación y tecnología

On-line version ISSN 2594-0732Print version ISSN 1405-7743

Ing. invest. y tecnol. vol.6 n.3 Ciudad de México Jul./Sep. 2005

Artículos

Solución numérica de problemas de valores en la frontera con alta exactitud por métodos espectrales

A. Camacho-Galván¹

B. Guardián-Soto²

M. Rodríguez-Green¹

^¹ Facultad de Ingeniería, UNAM, México. E-mail: abelcgmx@yahoo.com.mx

^² ESIME Culhuacán, IPN. México. E-mail: bdguardian@ipn.mx

Resumen

Entre la variedad de métodos disponibles para resolver problemas de valores en la frontera se cuentan los métodos espectrales, donde la solución u(x,t) de un cierto problema de valores en la frontera (dependiente de una variable espacial x y de una variable temporal), se aproxima por una suma finita vx,t=∑k=0Naktϕkx. Para este fin se debe, por una parte, seleccionar la clase de las funciones φ_k(x), k=1, ..., N, y por otra, prefijar los algoritmos adecuados para el desarrollo de los coeficientes a _k.

Palabras clave: Problemas de valores en la frontera; ecuaciones diferenciales en derivadas parciales; procesamiento paralelo; métodos pseudo espectrales

Abstract

Among the methods available for the solution of boundary problems we may find the so-called spectral methods, in which the solution u (x,t) (de pending upon a space-like variable x and a time-like variable) is approximated by afinite sum vx,t=∑k=0Naktϕkx.In order to have this form, on one hand, a class of functions φ_k(x), k=1, ..., N, has to be selected, and on the other, the ad equate algorithms for the expansion of the coefficients ak must be chosen.

Keywords: Numerical techniques; finite difference methods; collocation methods; Chebyshev approximation; Gauss-Lobatto points; Gauss-Radau points

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Recibido: Septiembre de 2004; Aprobado: Febrero de 2005

Este es un artículo publicado en acceso abierto bajo una licencia Creative Commons