Ecuación de Helmholtz generalizada

Autores/as

DOI:

https://doi.org/10.17268/sel.mat.2019.01.03

Palabras clave:

Ecuación de Helmholtz, funciones holomorfas

Resumen

En este artículo introducimos la ecuación de Helmholtz generalizada y presentamos soluciones explícitas para esta ecuación de Helmholtz generalizada, estas soluciones dependen de tres funciones holomorfas. Como aplicación presentamos soluciones explícitas para la ecuación de Helmholtz. Observamos que estas soluciones no
necesariamente estan limitadas a ciertos dominios del plano complejo C.

Citas

Bayliss, A. and Goldstein, C. The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics, Comput. Math. Appl. 1985; (11): 655–665.

Chu, L. Electromagnetic waves in elliptic hollow pipes of metal, J. Appl. Phys. 1938; (9): 583–591.

Gladwell, G. and Willms, N. On the mode shapes of the Helmholtz equation, J. Sound Vib. 1995; 188(3): 419–433.

Hirtum, A. V. Quasi-analytical solution of two-dimensional Helmholtz equation, Applied Mathematical Modelling, 2017; (47): 96–102.

Jones, D., Acoustic and Electromagnetic Waves, Clarendon Press, Oxford, UK, 1989.

Li, Zi-Cai, Wei, Y., Chen, Y. and Huang, Hung-Tsai. The method of fundamental solutions for the Helmholtz equation, Applied Numerical Mathematics, 2019; (135): 510–536.

Ma, J., Zhu, J. and Li, M. The Galerkin boundary element method for exterior problems of 2-D Helmholtz equation with arbitrary wavenumber, Engineering Analysis with Boundary Elements, 2010; (34): 1058–1063.

Porter, M. and Liboff, R. Vibrating quantum billiards on Riemannian manifolds, Int. J. Bifurc. Chaos, 2001; 11 (9): 2305–2315.

Rienstra, S. and Eversman, W. A numerical comparison between the multiple-scales and finite-element solution for sound propagation in lined flow ducts, J. Fluid Mech. 2001; (437): 367–384.

Sarkar, T. K., Chung, Y-S and Palma, M. S. Solution of the general Helmholtz equation starting from Laplace’s equation, ACES Journal, 2002, 17(3): 187–197.

Sukhorolskyi, M. A. Boundary- value problems for the Helmholtz equation in domains of the complex plane, Ukrainian Mathematical Journal, 2016; 68(3): 406–421.

Wilson, H. and Scharstein, R. Computing elliptic membrane high frequencies by Mathieu and Galerkin methods, J. Eng. Math. 2007; (57): 41–55.

Tsai, C., Young, D., Chiu, C. and Fan, C. Numerical analysis of acoustic modes using the linear least squares method of fundamental solutions, J. Sound Vib. 2009; (324): 1086–1110.

Wong, Y. and Li, G. Exact finite difference schemes for solving Helmholtz equation at any wavenumber, Int. J. Numer. Anal. Model. 2011; 2 (1): 91–108.

Publicado

2019-07-21

Cómo citar

C. Riveros, C. M., & V. Corro, A. M. (2019). Ecuación de Helmholtz generalizada. Selecciones Matemáticas, 6(01), 19-25. https://doi.org/10.17268/sel.mat.2019.01.03

Número

Sección

Articles

Artículos más leídos del mismo autor/a