African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 254

Full Length Research Paper

Existence of at least one solution of singular Volterra-Hammerstein integral equation and its numerical solution

R. T. Matoog
  • R. T. Matoog
  • Faculty of Applied Science, Umm Al– Qurah University, Makah, Kingdom of Saudi Arabia.
  • Google Scholar


  •  Received: 07 August 2016
  •  Accepted: 20 September 2016
  •  Published: 30 September 2016

References

Abdou MA (2003). On the solution of linear and nonlinear integral equation, Appl. Math. Comput. 146:857-871.
Crossref

 

Abdou MA, Badr AA, Soliman MB (2011). On a method for solving a two dimensional nonlinear integral equation of the second kind, J. CAM. 235:3589-3598.
Crossref

 
 

Abdou MA, El-Bore MM, El-Kojok MK (2009). Toeplitz matrix method for solving the nonlinear integral equation of Hammerstein type. J. Comp. Appl. Math. 223:765-776.
Crossref

 
 

Abdou MA, El-Kojak MK, Raad SA (2013b). Analytic and numeric solution of linear partial differential equation of fractional order, Global J. and Decision science. Ins. (USA) 13(3/10):57-71.

 
 

Abdou MA, El-Sayed WGEI, Deebs EI (2005). A solution of nonlinear integral equations, J. Appl. Math. Comput. 160:1-14.
Crossref

 
 

Abdou MA, Salama FA (2004). Volterra- Fredholm integral equation of the first kind and relationships, Appl. Math. Comput. 153:141-153
Crossref

 
 

Abdou MA, Al-Bigamy AM (2013a). Nonlinear Fredholm -Volterra integral equation and its numerical solutions with quadrature methods. J. Adv. Math. 14(2):415-422.

 
 

Arytiunian NKH (1959). A plane contact problem of creep theory, Appl. Math. Mech. 23(2):1041-1046.
Crossref

 
 

Atkinson KE (2011). The Numerical Solution of Integral Equations of the Second Kind, Cambridge, Cambridge University.

 
 

Bazm S, Babolian E (2012). Numerical solution of nonlinear two-dimensional Fredholm integral equations of the second kind using gauss product quadrature rules, Commun. Nonlinear Sci. Numer. Simult. 17:1215-1223.
Crossref

 
 

Diago T, Lima P (2008). Super convergence of collection methods for a class of weakly singular Volterra integral equation. J. Camp. Appl. Math. 218:307-331.
Crossref

 
 

Hacia L (1993). Approximate solution of Hammerstein equations. Appl. Anal. 50:277-284.
Crossref

 
 

Kaneko H, Xu Y (1996). Super convergence of the iterated Galerkin methods for Hammerstein equations SIAM, J. Num. Anal. 33:1048-1064.
Crossref

 
 

Kumar S (1988). A discrete collection-type method for Hammerstein equations. SIAMJ. Numb. Anal. 25:328-341.
Crossref

 
 

Kumar S, Sloan IH (1987). A new collection type method for Hammerstein integral equations, Math. Comput. 48:585-593.
Crossref

 
 

Lardy LJ (1981). A variation of Nystrom's method for Hammerstien equations. J. Integr. Equat. 3:43-60.

 
 

Vainikko G (2011). Spline collocation-interpolation method for linear and nonlinear cordial Volterra integral equations, Numer. Funct. Anal. Optim. 32:83-109.
Crossref

 
 

Zhang C, He Y (2008). The extended one – leg method for nonlinear neutral delay integro–differential equations, Appl. Numb. Math. 59:1409-1418.
Crossref