TY - JOUR AU - Alipour, Mohsen AU - Rostamy, Davood PY - 2011 TI - Bernstein Polynomials for Solving Abels Integral Equation JO - Journal of Mathematics and Computer Science SP - 403--412 VL - 3 IS - 4 AB - This paper presents a numerical method for solving Abel’s integral equation as singular Volterra integral equations. In the proposed method, the functions in Abel’s integral equation are approximated based on Bernstein polynomials (BPs) and therefore, the solving of Abel’s integral equation is reduced to the solving of linear algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.03.04.06 DO - 10.22436/jmcs.03.04.06 ID - Alipour2011 ER - TY - BOOK TI - Abel integral equations: analysis and applications AU - R. Goreno AU - S. Vessella PB - Springer-Verlag PY - 1991 DA - 1991// CY - Berlin-New York ID - Goreno1991 ER - TY - JOUR TI - Sur quelques points de la theorie de l’equation integrale d’Abel AU - N. Zeilon JO - Arkiv. Mat. Astr. Fysik. PY - 1922 DA - 1922// VL - 18 ID - Zeilon 1922 ER - TY - BOOK TI - Integral Equations AU - F. G. Tricomi PB - Dover Publications PY - 1985 DA - 1985// CY - New York ID - Tricomi1985 ER - TY - JOUR TI - A variation of Nystrom’s method for Hammerstein equations AU - L. J. Lardy JO - J. Integ. Equat. PY - 1981 DA - 1981// VL - 3 ID - Lardy1981 ER - TY - JOUR TI - A new collocation-type method for Hammerstein integral equations AU - S. Kumar AU - I. H. Sloan JO - J. Math. Comput. PY - 1987 DA - 1987// VL - 48 ID - Kumar1987 ER - TY - JOUR TI - Implicitly linear collocation method for nonlinear Volterra equations AU - H. Brunner JO - J. Appl. Num. Math. PY - 1992 DA - 1992// VL - 9 ID - Brunner1992 ER - TY - JOUR TI - Asymptotic error expansion variation of a collocation method for Volterra–Hammerstein equations AU - H. Guoqiang JO - J. Appl. Num. Math. PY - 1993 DA - 1993// VL - 13 ID - Guoqiang1993 ER - TY - JOUR TI - A new approach to the numerical solution of weakly singular Volterra integral equations AU - P. Baratella AU - A. P. Orsi JO - J. Computat. Appl. Math. PY - 2004 DA - 2004// VL - 163 ID - Baratella2004 ER - TY - BOOK TI - Introduction Functional Analysis with Applications AU - E. Kreyszig PB - John Wiley & Sons PY - 1978 DA - 1978// CY - U.S.A. ID - Kreyszig1978 ER - TY - BOOK TI - A First Course in Integral Equations AU - A. M. Wazwaz PB - World Scientific Publishing Company PY - 1997 DA - 1997// CY - New Jersey ID - Wazwaz1997 ER -