Abstract
The aim of present article is to find the approximate solution of integral equation using Bernstein multiwavelets approximation. Bernstein polynomial multiwavelets are constructed using orthonormal Bernstein polynomials. These Bernstein polynomial multiwavelets approximate the solution of integral equation. Using orthogonality property of Bernstein polynomial muliwavelets operational matrix of integration is obtained which reduces the integral equation in the system of algebraic equation and can be solved easily. The examples of different profiles are illustrated.
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References
Abel, N.H.: Resolution d’un problemde mechanique. J. Reine. Angew. Math. 1, 153–157 (1826)
Mach, L.: Wien Akad. Ber. Math. Phys. Klasse 105, 605 (1896)
Jakeman, A.J., Anderssen, R.S.: Abel type integral equations in stereology I. General discussion. J. Microsc. 105, 121–133 (1975)
Healy, S.B., Haase, J., Lesne, O.: Abel transform inversion of radio occultation measurements made with a receiver inside the Earth’s atmosphere. Annal. Geophys. 20, 1253–1256 (2002)
Solomon, S.C., Hays, P.B., Abreu, V.J.: Tomographic inversion of satellite photometry. Appl. Opt. 23, 3409–3414 (1984)
Kosarev, E.L.: Applications of integral equations of the first kind in experiment physics. Comput. Phys. Commun. 20, 69–75 (1980)
Buck, U.: Inversion of molecular scattering data. Rev. Mod. Phys. 46, 369–389 (1974)
Hellsten, H., Andersson, L.E.: An inverse method for the processing of synthetic apertureradar data. Inverse Prob. 3, 111–124 (1987)
Anderssen, R.S., Calligaro, R.B.: Non destructive testing of optical-fiber preforms. J. Aust. Math. Soc. (Ser B) 23, 127–135 (1981)
Glantschnig, W.J.: How accurately can one reconstruct an index profile from transverse measurement data. IEEE J. Lightwave Technol. 3, 678–683 (1985)
Keren, E., Bar-Ziv, E., Glatt, I., Kafri, O.: Measurements of temperature distributionof flames by moiré deflectometry. Appl. Opt. 20, 4263–4266 (1981)
Tallents, C.J., Burgess, M.D.J., Luther-Davies, B.: The determination of electrondensity profiles from refraction measurements obtained using holographic interferometry. Opt. Commun. 44, 384–387 (1983)
Fleurier, C., Chapelle, J.: Inversion of Abel’s integral equation application to plasma spectroscopy. Comput. Phys. Commun. 7, 200–206 (1974)
Yousefi, S.A.: B-Polynomial multiwavelets approach for solution of Abel’s integral equation. Int. J. Comp. Math. 87, 310–316 (2010)
Yousefi, S.A.: Numerical solution of Abel’s integral equation by using Legendrewavelets. Appl. Math. Comput. 175, 574–580 (2006)
Bhattacharya, S., Mandal, B.N.: Use of Bernstein polynomials in numerical solutions of Volterra integral equations. Appl. Math. Scien. 2(36), 1773–1787 (2008)
Mohammad, P., Ali, T., Morteza, M.G., Saboori, S.: Wavelet compression of ECG signal using SPIHT algorithm. Int. J. Inf Com Eng. 2, 219 (2005)
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Suman, S., Singh, K.K., Pandey, R.K. (2014). Approximate Solution of Integral Equation Using Bernstein Polynomial Multiwavelets. In: Pant, M., Deep, K., Nagar, A., Bansal, J. (eds) Proceedings of the Third International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 259. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1768-8_43
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DOI: https://doi.org/10.1007/978-81-322-1768-8_43
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