An approximate solution of integral equation using Bezier control Points

Document Type : Research Paper

Authors

1 College of Engineering, Al-Nahrain University, Baghdad, Iraq

2 Department of Mathematics, College of Science for woman, University of Baghdad,Iraq

3 College of Engineering Al-musayab, Department of Energy Engineering, University of Babylon, Iraq

Abstract

 The integral equations are computed numerically using a Bezier curve. We have written the  linear  Fredholm integral equation into a matrix formulation by using a Bezier curves as a piecewise polynomials of degree n and we use (n+1) unknown control points on unit interval to determine Bezier curve. two examples have been discussed in details.

Keywords

[1] M. Abdou, On asymptotic methods for redholm-volterra integral equation of the second kind in contact problems, J. Computational and Appl. Math. 145 (2003) 431–446.
[2] M. Evrenosoglu and S. Somali, Least squares methods for solving singularly perturbed two-point boundary value problems using Bezier control points, App. Math. Lett. 21 (2008) 1029–1032.
[3] K. Forbes, S. Crozier and D. Doddrell, Calculating current densities and fields produced by shielded magnetic resonance imagingprobes, SIAM J. Math. Anal. 57 (1997) 401–425.
[4] F. Ghomanjani, M. Farahi and A. Kilicman, Bezier curves for solving Fredholm integral equations of the second kind, Math. Prob. Engin. 6 (2014).
[5] K. Harada and E. Nakamae, Application of the Bezier curve to data interpolation, Comput. Aided Des. 14 (1982) 55–59.
[6] K. Holmaker, Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones, SIAM J. Math. Anal. 24 (1993) 116–128.
[7] A. Jerri, Introduction to Integral Equations with Application, John Wiley & Sons Inc., 1999.
[8] E. Kreyszig, Bernstein polynomials and numerical integration, Int. J. Numer. Method Engin. 14 (1979) 292–295.
[9] G. Nurnberger and F. Zeilfelder, Developments in bivariate spline interpolation, J. Comput. Appl. Math. 121 (2000) 125–152.
[10] J. Reinkenhof, Differentiation and integration using Bernstein’s polynomials, Int. J. Numer. Methods Engin. 11(10) (1977) 1627–1630.
[11] S. Swarup, Integral E quations, Krishna Prakashan Media Pvt. LTD, 15th Edition, 2007.
[12] J. Zheng, T. Sederberg and R. Johnson, Least squares methods for solving differential equations using Bezier control points, Appl. Num. Math. 48 (2004) 237–252.
Volume 12, Issue 2
November 2021
Pages 793-798
  • Receive Date: 10 February 2021
  • Revise Date: 17 March 2021
  • Accept Date: 19 April 2021