Chebyshev polynomial solution of the system of Cauchy-type singular integral equations of the first kind. (English) Zbl 1278.65204
From the authors’ abstract: The paper presents a Chebyshev series method for the numerical solution of a system of a Chauchy-type singular integral equation (SIE) of the first kind. Chebyshev polynomials of the second type with corresponding weight functions are used to approximate the density functions. It is shown that the numerical solution of the system of characteristic SIEs is identical to the exact solution when the force functions are cubic.
Reviewer: Ludwig Kohaupt (Berlin)
MSC:
| 65R20 | Numerical methods for integral equations |
| 45E05 | Integral equations with kernels of Cauchy type |
Keywords:
characteristic singular integral equation; Chebyshev polynomials; Chebyshev series expansion; Chauchy-type singular integral equationReferences:
| [1] | Abdulkawi M., IJMCS 5 pp 90– (2009) |
| [2] | Abdulkawi M., Eur. J. Pure Appl. Math. 2 pp 462– (2009) |
| [3] | Aleksandrov V. M., Problems of Continuum Mechanics with Mixed Boundary Conditions (1986) |
| [4] | Belocerkovski, S. M. and Lifanov, I. K. 1985. ”Numerical Methods for singular Integral Equations and its Applications in Aerodynamics”. Nauka, Moskov: Theory of Elastisity and Electrodynamics. (in Russian) |
| [5] | DOI: 10.1016/S0893-9659(04)90125-5 · Zbl 1061.65141 · doi:10.1016/S0893-9659(04)90125-5 |
| [6] | Erdelyi, A. 1953. ”Higher Transcendental Functions”. Edited by: Erdelyi, A. Vol. 2, New York: McGraw-Hill. |
| [7] | Erdogan F., Q. J. Appl. Math. 29 pp 525– (1972) · Zbl 0236.65083 · doi:10.1090/qam/408277 |
| [8] | Erdogan F., Methods of Analysis and Solutions of Crack Problems pp 368– (1973) · doi:10.1007/978-94-017-2260-5_7 |
| [9] | DOI: 10.1016/j.aml.2008.08.001 · Zbl 1161.65370 · doi:10.1016/j.aml.2008.08.001 |
| [10] | Ioakimidis N. I., Serdica Bulgaricae Mathematica Publicationes 10 pp 78– (1984) |
| [11] | Kim S., Appl. Math. Comput. 35 pp 63– (1998) · Zbl 0999.65149 · doi:10.1016/S0898-1221(98)00073-X |
| [12] | Lifanov, L. K. 1996. ”One dimensional singular integral equations, in Singular Integral Equation and Discrete Vortices”. Edited by: Lifanov, L. K. 45–53. The Netherland: VSO. Chap. 2 |
| [13] | DOI: 10.1098/rspa.1989.0014 · Zbl 0674.73071 · doi:10.1098/rspa.1989.0014 |
| [14] | Mason J. C., Chebyshev Polynomials (2003) |
| [15] | Miller G. R., Q. J. Appl. Math. 43 pp 455– (1985) · Zbl 0593.65094 · doi:10.1090/qam/766882 |
| [16] | Muskheleshvili, N. I. 2008.Singular integral equations with Cauchy type kernels,inSingular Integral Equations, Edited by: Radok, J. R.M. 123–128. New York: Dover Publications. Chap. 6 |
| [17] | Savruk M. P., Naukova dumka, Kiev (1989) |
| [18] | Schlichting H., Aerodynamics of the Airplane (1979) |
| [19] | Sheshko M., Singular Integral Equations with Cauchy and Hilbert Kernels and theirs Approximated Solutions (2003) |
| [20] | Srivastav R. P., Appl. Math. Comput. 21 pp 59– (1991) · Zbl 0725.65135 · doi:10.1016/0898-1221(91)90125-N |
| [21] | Theocaris P. S., Bull. Calcutta Math. Soc. 71 pp 29– (1978) |
| [22] | DOI: 10.1080/00036817908839250 · Zbl 0404.65068 · doi:10.1080/00036817908839250 |
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