Year 2019, Volume 48 , Issue 6, Pages 1729 - 1743 2019-12-08

Solving Fredholm integral equations of the first kind by using wavelet bases

Yaser ROSTAMİ [1] , Khosrow Maleknejad [2]


In this paper, we used a project technique for solving integral equation of the first kind by wavelet families via regularization approach and we proved the convergence for the numerical method and error consideration. Semi-orthogonal B-spline scaling functions and wavelets of degree 4 and their dual functions are presented to approximate the solutions to integral equations. Sparse matrix will product of semi-orthoganality and vanishing moment properties of B-spline wavelets.
Fredholm integral equations, projection method, regularization, quartic B-spline wavele
  • [1] H. Adibi and P. Assari, Chebyshev wavelet method for numerical solution of Fredholm integral equation of the first kind, Math. Prob. Eng, 2010, Article ID 138408, 17 pp., 2010.
  • [2] K. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press 2, 1997.
  • [3] C.K. Chui, L. Montefusco and L. Puccio, Wavelets, Theory algorithm and applications, Academic press, 1994.
  • [4] A. Cohen, Numerical Analysis of Wavelet Methods, New York, Academic Press, 2003.
  • [5] P.K. Kythe and P. Puri, Computational Methods for Linear Integral Equations, Springer Science, 2002.
  • [6] K. Maleknejad, T. Lotfi and K. Mahdiani, Numerical solution of first kind Fredholm integral equation with wavelets-Galerkin method (WGM) and wavelets precondition, Appl. Math. Comput. 186, 794-800, 2007.
  • [7] K. Maleknejad, T. Lotfi and Y. Rostami, Numerical Computational Method in Solving Fredholm Integral Equations of the Second Kind by Using Coifman Wavelet, Appl. Math. Comput. 186, 212-218, 2007.
  • [8] K. Maleknejad, H. Mesgarani and T. Nikazad, Wavelet-Galerkin Solutions For Fredholm Integral Equations of The Second Kind, Internat. J. Engng. Sci. 13, 75-80, 2002.
  • [9] K. Maleknejad and S. Sohrabi,Numerical solution of Fredholm integral equation of the first kind by using Legendre wavelets, Appl. Math. Comput. 186, 836-843, 2007.
  • [10] M.T. Rashed, Numerical solutions of the integral equations of the first kind, Appl. Math. Comput. 2-3 , 413-420, 2003.
  • [11] P.K. Sahu and S. Saha Ray, Numerical solutions for the system of Fredholm integral equations of second kind by a new approach involving semiorthogonal B-spline wavelet collocation method. Appl. Math. Comput. 234, 368-379, 2014.
  • [12] M. Shamsi and M. Razzaghi, Solution of Hallens integral equation using multiwavelets, Comput. Phys. Comm. C 168, 187-197, 2015.
  • [13] A.M. Wazwaz, The regularization method for Fredholm integral equations of the first kind, Comput. Math. Appl. 61 (10), 2981-2986, 2011.
  • [14] G.A. Zakeri and M. Navab, Sinc collocation approximation of non-smooth solution of a nonlinear weakly singular Volterra integral equation, J. Comput. Phys. 229, 6548-6557, 2010.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-4506-9672
Author: Yaser ROSTAMİ
Institution: Islamic Azad University
Country: Iran


Orcid: 0000-0003-1774-7525
Author: Khosrow Maleknejad
Institution: Iran University of Science and Technology
Country: Iran


Dates

Publication Date : December 8, 2019

Bibtex @research article { hujms553433, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1729 - 1743}, doi = {10.15672/hujms.553433}, title = {Solving Fredholm integral equations of the first kind by using wavelet bases}, key = {cite}, author = {ROSTAMİ, Yaser and Maleknejad, Khosrow} }
APA ROSTAMİ, Y , Maleknejad, K . (2019). Solving Fredholm integral equations of the first kind by using wavelet bases. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1729-1743 . DOI: 10.15672/hujms.553433
MLA ROSTAMİ, Y , Maleknejad, K . "Solving Fredholm integral equations of the first kind by using wavelet bases". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1729-1743 <https://dergipark.org.tr/en/pub/hujms/issue/50516/553433>
Chicago ROSTAMİ, Y , Maleknejad, K . "Solving Fredholm integral equations of the first kind by using wavelet bases". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1729-1743
RIS TY - JOUR T1 - Solving Fredholm integral equations of the first kind by using wavelet bases AU - Yaser ROSTAMİ , Khosrow Maleknejad Y1 - 2019 PY - 2019 N1 - doi: 10.15672/hujms.553433 DO - 10.15672/hujms.553433 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1729 EP - 1743 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.553433 UR - https://doi.org/10.15672/hujms.553433 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Solving Fredholm integral equations of the first kind by using wavelet bases %A Yaser ROSTAMİ , Khosrow Maleknejad %T Solving Fredholm integral equations of the first kind by using wavelet bases %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/hujms.553433 %U 10.15672/hujms.553433
ISNAD ROSTAMİ, Yaser , Maleknejad, Khosrow . "Solving Fredholm integral equations of the first kind by using wavelet bases". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1729-1743 . https://doi.org/10.15672/hujms.553433
AMA ROSTAMİ Y , Maleknejad K . Solving Fredholm integral equations of the first kind by using wavelet bases. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1729-1743.
Vancouver ROSTAMİ Y , Maleknejad K . Solving Fredholm integral equations of the first kind by using wavelet bases. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1743-1729.