×

Numerical solution of the one-dimensional wave equation with an integral condition. (English) Zbl 1112.65097

Summary: The hyperbolic partial differential equation with an integral condition arises in many physical phenomena. In this research a numerical technique is developed for the one-dimensional hyperbolic equation that combines classical and integral boundary conditions. The proposed method is based on a shifted Legendre tau technique. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bouziani, Int J Math Math Sci 30 pp 327– (2002)
[2] , and , Mathematical problems in viscoelasticity, Longman Science and Technology, England, 1987. · Zbl 0719.73013
[3] Beilin, Electronic J Differential Eq 76 pp 1– (2001)
[4] Bouziani, Acad Roy Belg Bull CI Sci 6 pp 389– (1994)
[5] Mesloub, Intern J Math Math Sci 22 pp 511– (1999)
[6] Pulkina, Electronic J Differential Eq 45 pp 1– (1999)
[7] Pulkina, Differets Uravn VN 2 pp 1– (2000)
[8] Gordeziani, Matem Modelirovani 12 pp 94– (2000)
[9] Muravei, Matem Zametki 54 pp 98– (1993)
[10] Kavalloris, Appl Math E-Notes 2 pp 59– (2002)
[11] Ang, SEA Bull Math 26 pp 197– (2002)
[12] Cannon, Intern J Engng Sci 28 pp 579– (1990)
[13] Cannon, Quart Appl Math 21 pp 155– (1963)
[14] The one dimensional heat equation, Encyclopedia of Mathematics and its Applications, Vol. 23, Addison-Welsey, Menlo Park, CA, 1984. · doi:10.1017/CBO9781139086967
[15] Cannon, Annali Di Mat Pura ed Appl 130 pp 385– (1982)
[16] Dehghan, Appl Math Comput 145 pp 185– (2003)
[17] Dehghan, Int J Computer Math 81 pp 25– (2004)
[18] Dehghan, Appl Numer Math 52 pp 39– (2005)
[19] Ekolin, BIT 31 pp 245– (1991)
[20] Saadatmandi, Int J Computer Math 81 pp 1427– (2004)
[21] Lin, J Comput Appl Math 47 pp 335– (1993)
[22] Lin, Int J Engng Sci 32 pp 395– (1994)
[23] Bouziani, Hiroshima Math J 27 pp 373– (1997)
[24] Dehghan, Numer Methods Partial Differential Eq 21 pp 24– (2005)
[25] Dehghan, Comm Numer Methods Engrg 19 pp 65– (2003)
[26] Ang, Appl Numer Math 56 pp 1054– (2006)
[27] Applied analysis, Prentice-Hal, Englewood Cliffs, NJ, 1956.
[28] , , and , Spectral methods in fluid dynamic, Prentice-Hall, Englewood Cliffs, NJ, 1988. · doi:10.1007/978-3-642-84108-8
[29] , and , Theory and applications of spectral methods, Spectral methods for partial differential equations, , and , editors, SIAM, Philadelphia, 1984.
[30] Dehghan, Numer Methods Partial Differential Eq 22 pp 220– (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.