Bernstein series solution of a class of linear integro-differential equations with weakly singular kernel

Applied Mathematics and Computation

Volumn 217, Issue 16, 2011, Pages 7009-7020

  Işik, Osman Raşit ^a   Sezer, Mehmet ^a   Güney, Zekeriya ^a  

^a MUGLA SITKI KOCMAN UNIVERSITY   (Turkey)

Author keywords

Abels integral equations; Bernstein polynomials; Integro differential equations; Singular volterra integral equations; Volterra equations

Indexed keywords

ABELS INTEGRAL EQUATIONS; APPROXIMATE SOLUTION; BERNSTEIN POLYNOMIAL; BERNSTEIN POLYNOMIALS; COLLOCATION METHOD; EXACT SOLUTION; LINEAR INTEGRO-DIFFERENTIAL EQUATIONS; SERIES SOLUTIONS; STABILITY ANALYSIS; VOLTERRA EQUATION; VOLTERRA INTEGRAL EQUATIONS; VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS; WEAKLY SINGULAR KERNEL;

INTEGRODIFFERENTIAL EQUATIONS;

POLYNOMIALS;

EID: 79952450721     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.01.114     Document Type: Article

References (16)

1. M. Sezer Taylor polynomial solution of Volterra integral equations Int. J. Math. Edu. Sci. Technol. 25 5 1994 625 633
2. S. Yalinba, and M. Sezer The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials Appl. Math. Comput. 112 2000 291 308
3. R.P. Kanwal, and K.C. Liu Taylor expansion approach for solving integral equations Int. J. Math. Edu. Sci. Technol 20 3 1989 411 414
4. Y. Huang, and X.-F. Li Approximate solution of a class of linear integro-differential equations by Taylor expansion method Int. J. Comput. Math. 2009 1 12
5. A.J. Jakeman, and R.S. Anderssen Abel type integral equations in stereology I. General discussion J. Microsci. 105 1975 121 133
6. J.B. Macelwane Evidence on the interior of the earth derived from seismic sources B. Gutenberg, Internal Constitution of the Earth 1951 Dover New York 227 304
7. S.B. Healy, J. Haase, and O. Lesne Abel transform inversion of radio occultation measurements made with a receiver inside the Earths atmosphere Annal. Geophys. 20 2002 253 1256
8. R.N. Bracewell, and A.C. Riddle Inversion of fan-beam scans in radio astronomy Astrophys. J. 150 1967 427 434
9. U. Buck Inversion of molecular scattering data Rev. Mod. Phys. 46 1974 369 389
10. E.L. Kosarev Applications of integral equations of the first kind in experiment physics Comput. Phys. Commun. 20 1980 69 75
11. S.A. Yousefi Numerical solution of Abels integral equation by using Legendre wavelets Appl. Math. Comput. 175 2006 574 580
12. V.K. Singh, R.K. Pandey, and O.P. Singh New stable numerical solutions of Singular integral equations of Abel type by using normalized Bernstein polynomials Appl. Math. Sci. 3 5 2009 241 255
13. M. Idrees Bhatti, and P. Bracken Solutions of differential equations in a Bernstein polynomial basis J. Comput. Appl. Math. 205 2007 272 280 (Pubitemid 46636072)
14. A. Quarteroni, R. Sacco, and F. Saleri Numerical Mathematics 2007 Springer N.Y.
15. T.J. Rivlin An Introduction to the Approximation of Functions 2003 Dover Publications N.Y.
16. George M. Phillips Interpolation and Approximation by Polynomials 2003 Springer N.Y