×

Hartley series approximations for the parabolic equations. (English) Zbl 1075.65128

Summary: An approximate method for solving parabolic equations with a periodic boundary condition is proposed. The method is based upon using the Legendre series and the Hartley series to approximate the required solution. The parabolic equations are converted into a system of linear algebraic equations which can be solved for the unknown coefficients. A numerical example is included to demonstrate the validity and applicability of the method and a comparison is made with existing results.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1080/00207177508922043 · Zbl 0308.49035 · doi:10.1080/00207177508922043
[2] DOI: 10.1080/00207178108922979 · Zbl 0464.93027 · doi:10.1080/00207178108922979
[3] DOI: 10.1007/BF00934611 · Zbl 0481.49005 · doi:10.1007/BF00934611
[4] DOI: 10.1007/BF00934535 · Zbl 0481.49004 · doi:10.1007/BF00934535
[5] DOI: 10.1080/00207728508926718 · Zbl 0568.49019 · doi:10.1080/00207728508926718
[6] DOI: 10.1080/00207178808906224 · Zbl 0651.49012 · doi:10.1080/00207178808906224
[7] DOI: 10.1049/ip-cta:19970702 · Zbl 0880.93014 · doi:10.1049/ip-cta:19970702
[8] DOI: 10.1080/00207729808929544 · doi:10.1080/00207729808929544
[9] DOI: 10.1109/61.193891 · doi:10.1109/61.193891
[10] Zhang F. Y., Journal of Computational Mathematics 16 pp 107–
[11] DOI: 10.1137/0726001 · Zbl 0668.65090 · doi:10.1137/0726001
[12] DOI: 10.1137/0715059 · Zbl 0434.65091 · doi:10.1137/0715059
[13] Eriksson K., RAIRO Analyse Numerique 19 pp 611– (1985)
[14] Babuska I., Numerical Methods for Partial Differential Equations 5 pp 363– · Zbl 0693.65078 · doi:10.1002/num.1690050407
[15] Canute C., Spectral Methods in Fluid Dynamics (1987)
[16] Lancaster P., Theory of Matrices (1969) · Zbl 0186.05301
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.