Numerical solution of nonlinear Volterra–Fredholm integral equations using hybrid of block-pulse functions and Taylor series

Abstract A numerical method based on an NM-set of general, hybrid of block-pulse function and Taylor series (HBT), is proposed to approximate the solution of nonlinear Volterra–Fredholm integral equations. The properties of HBT are first presented. Also, the operational matrix of integration together with Newton-Cotes nodes are utilized to reduce the computation of nonlinear Volterra–Fredholm integral equations into some algebraic equations. In addition, convergence analysis and numerical examples that illustrate the pertinent features of the method are presented.

[1]  Khosrow Maleknejad,et al.  Triangular functions (TF) method for the solution of nonlinear Volterra–Fredholm integral equations , 2010 .

[2]  Khosrow Maleknejad,et al.  Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functions , 2004, Appl. Math. Comput..

[3]  Yadollah Ordokhani,et al.  Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via rationalized Haar functions , 2006, Appl. Math. Comput..

[4]  M. Thoma,et al.  Block Pulse Functions and Their Applications in Control Systems , 1992 .

[5]  O. Diekmann,et al.  Thresholds and travelling waves for the geographical spread of infection , 1978, Journal of mathematical biology.

[6]  Han Guo-qiang,et al.  Asymptotic expansion for the trapezoidal Nystro¨m method of linear Volterra-Fredholm equations , 1994 .

[7]  Khosrow Maleknejad,et al.  Hybrid functions approach for the nonlinear Volterra-Fredholm integral equations , 2011, WCIT.

[8]  Esmail Babolian,et al.  Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method , 2007, Appl. Math. Comput..

[9]  Salih Yalçinbas.  Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations , 2002, Appl. Math. Comput..

[10]  Mohsen Razzaghi,et al.  Legendre wavelets method for the nonlinear Volterra-Fredholm integral equations , 2005, Math. Comput. Simul..

[11]  H. Almasieh,et al.  Triangular functions method for the solution of Fredholm integral equations system , 2012 .

[12]  Mohsen Razzaghi,et al.  Solution of multi-delay systems using hybrid of block-pulse functions and Taylor series , 2006 .

[13]  Yadollah Ordokhani,et al.  Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via a collocation method and rationalized Haar functions , 2008, Appl. Math. Lett..

[14]  Mohsen Razzaghi,et al.  Optimal control of linear distributed-parameter systems via polynomial series , 1989 .

[15]  L. Delves,et al.  Computational methods for integral equations: Frontmatter , 1985 .

[16]  Ahmad Golbabai,et al.  Modified homotopy perturbation method for solving non-linear Fredholm integral equations , 2009 .

[17]  G. Phillips,et al.  Theory and application of numerical analysis , 1973 .

[18]  H. Brunner.  On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods , 1990 .

[19]  L. Hacia.  On approximate solution for integral equations of the mixed type , 1996 .

[20]  Z. Masouri,et al.  Numerical expansion-iterative method for analysis of integral equation models arising in one- and two-dimensional electromagnetic scattering , 2012 .