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Yuksel, Gamze; Isik, Osman Rasit; Sezer, Mehmet

Error analysis of the Chebyshev collocation method for linear second-order partial differential equations. (English) Zbl 1325.65141

Int. J. Comput. Math. 92, No. 10, 2121-2138 (2015).
Summary: The purpose of this study is to apply the Chebyshev collocation method to linear second-order partial differential equations (PDEs) under the most general conditions. The method is given with a priori error estimate which is obtained by polynomial interpolation. The residual correction procedure is modified to the problem so that the absolute error may be estimated. Finally, the effectiveness of the method is illustrated in several numerical experiments such as Laplace and Poisson equations. Numerical results are overlapped with the theoretical results.

Cited in 6 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35G05 Linear higher-order PDEs

Keywords:

partial differential equations; Chebyshev collocation method; Chebyshev polynomial solutions; error analysis of collocation methods; residual correction procedure
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\textit{G. Yuksel} et al., Int. J. Comput. Math. 92, No. 10, 2121--2138 (2015; Zbl 1325.65141)
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References:

[1] DOI: 10.1080/00207169908804871 · Zbl 0947.65142
[2] DOI: 10.1016/S0096-3003(03)00334-5 · Zbl 1049.65149
[3] DOI: 10.1016/j.amc.2006.01.018 · Zbl 1148.65318
[4] DOI: 10.1002/num.20362 · Zbl 1167.65067
[5] DOI: 10.1007/978-0-387-68918-0 · Zbl 1135.65014
[6] DOI: 10.1017/CBO9780511626340
[7] DOI: 10.1016/j.amc.2005.05.019 · Zbl 1090.65096
[8] DOI: 10.1002/fld.2316 · Zbl 1432.76283
[9] DOI: 10.1016/j.amc.2004.11.038 · Zbl 1082.65556
[10] DOI: 10.1016/j.amc.2008.09.038 · Zbl 1157.65431
[11] DOI: 10.1016/j.mcm.2011.01.011 · Zbl 1219.65106
[12] DOI: 10.1016/j.cam.2004.11.015 · Zbl 1071.65136
[13] DOI: 10.1016/S0378-4754(01)00421-9 · Zbl 1004.65120
[14] DOI: 10.1137/1.9781611970425
[15] Işık O.R., Math. Methods Appl. Sci
[16] DOI: 10.1016/S0096-3003(01)00273-9 · Zbl 1029.35055
[17] DOI: 10.1016/j.camwa.2008.03.013 · Zbl 1155.65381
[18] DOI: 10.1016/S0377-0427(99)00306-4 · Zbl 0962.76071
[19] DOI: 10.1016/j.cam.2007.11.007 · Zbl 1153.65102
[20] DOI: 10.1016/j.cam.2008.09.011 · Zbl 1165.65081
[21] DOI: 10.1002/num.20417 · Zbl 1186.65152
[22] Mason J.C., Chebyshev Polynomials (2003)
[23] DOI: 10.1007/BF01395986 · Zbl 0431.65056
[24] Quarteroni A., Numerical Mathematics (2007) · Zbl 1136.65001
[25] Sezer M., J. Fac. Sci. Engrg. Univ 12 pp 69– (1989)
[26] DOI: 10.1080/0020739960270503 · Zbl 0884.65134
[27] DOI: 10.1080/0020739960270414 · Zbl 0887.34012
[28] Smith G.D., Numerical Solution of Partial Differential Equations: Finite Difference Methods (1985) · Zbl 0576.65089
[29] Süli E., Lecture Notes on Finite Element Methods for Partial Differential Equations (2012)
[30] DOI: 10.1016/j.amc.2005.04.015 · Zbl 1090.65134
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.