Bernstein polynomials for solving Abel's integral equation

被引：25

作者：

Alipour, Mohsen ^{[1
]}

Rostamy, Davood ^{[2
]}

机构：

[1] Islam Azad Univ, Member young Res club, Sari branch, POB 48164-194, Sari, Iran

[2] Imam Khomeini Int Univ, Dept Math, Qazvin, Iran

来源：

JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS | 2011年 / 3卷 / 04期

关键词：

Abel's integral equations; Singular Volterra integral equations; Bernstein polynomials;

D O I：

10.22436/jmcs.03.04.06

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：403 / 412

页数：10

共 9 条

[1] A new approach to the numerical solution of weakly singular Volterra integral equations [J].

Baratella, P ;

Orsi, AP .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 163 (02) :401-418

[2] IMPLICITLY LINEAR COLLOCATION METHODS FOR NONLINEAR VOLTERRA-EQUATIONS [J].

BRUNNER, H .

APPLIED NUMERICAL MATHEMATICS, 1992, 9 (3-5) :235-247

[3]

Goren~o R., 1991, ABEL INTEGRAL EQUATI

[4]

Guoqiang H, 1993, APPL NUMER MATH, V13, P357, DOI DOI 10.1016/0168-9274(93)90094-8

[5]

Kumar S., 1987, J MATH COMPUT, V48, P123, DOI [10.1090/S0025-5718-1987-0878692-4, DOI 10.1090/S0025-5718-1987-0878692-4]

[6]

LARDY LJ, 1981, J INTEGRAL EQUAT, V3, P43

[7]

Tricomi F.G., 1982, INTEGRAL EQUATIONS

[8]

Wazwaz A.M, 1997, 1 COURSE INTEGRAL EQ

[9]

Zeilon N., 1924, ARK MAT ASTR FYSIK, V18, P1

← 1 →