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Ahdiaghdam, S.; Shahmorad, S.; Ivaz, K.

Approximate solution of dual integral equations using Chebyshev polynomials. (English) Zbl 1365.65276

Int. J. Comput. Math. 94, No. 3, 493-502 (2017).
Summary: The aim of the present work is to introduce solution of special dual integral equations by the orthogonal polynomials. We consider a system of dual integral equations with trigonometric kernels which appear in formulation of the potential distribution of an electrified plate with mixed boundary conditions and convert them to Cauchy-type singular integral equations. We use the Chebyshev orthogonal polynomials to construct approximate solution for Cauchy-type singular integral equations which will solve the main dual integral equations. Numerical results demonstrate effectiveness of this method.

Cited in 4 Documents

MSC:

65R20 Numerical methods for integral equations
45F10 Dual, triple, etc., integral and series equations
45E05 Integral equations with kernels of Cauchy type

Keywords:

dual integral equations; Fourier transform; trigonometric kernels; Cauchy-type singular integral equations; numerical results
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[1] DOI: 10.1002/(SICI)1521-4001(200003)80:3<205::AID-ZAMM205>3.0.CO;2-8 · doi:10.1002/(SICI)1521-4001(200003)80:3<205::AID-ZAMM205>3.0.CO;2-8
[2] DOI: 10.1016/S0893-9659(04)90125-5 · Zbl 1061.65141 · doi:10.1016/S0893-9659(04)90125-5
[3] DOI: 10.4236/am.2014.54072 · doi:10.4236/am.2014.54072
[4] DOI: 10.1016/j.aml.2008.08.001 · Zbl 1161.65370 · doi:10.1016/j.aml.2008.08.001
[5] DOI: 10.1080/00207168108803258 · Zbl 0473.65100 · doi:10.1080/00207168108803258
[6] Jerry A.J., Introduction to Integral Equations with Applications, 2. ed. (1999)
[7] DOI: 10.1016/j.aml.2006.05.005 · Zbl 1158.45300 · doi:10.1016/j.aml.2006.05.005
[8] Mason J.C., Chebyshev Polynomials (2003)
[9] Nasim C., Indian J. Pure Appl. Math. 15 (3) pp 323– (1984)
[10] DOI: 10.1201/9781420010558 · doi:10.1201/9781420010558
[11] DOI: 10.1017/s2040618500034006 · Zbl 0118.31402 · doi:10.1017/s2040618500034006
[12] Snyder M.N., Chebyshev Methods in Numerical Approximation (1966) · Zbl 0173.44102
[13] Wrede R., Schaum’s Outline Series, in: Advanced Calculus, 3. ed. (2010)
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