Numerical solution of Hammerstein Fredholm and Volterra integral equations of the second kind using block pulse functions and collocation method

Subject Areas : Applied Mathematics

M. M.  Shamivand ¹ (Department of Mathematics, Islamic Azad University, Borujerd Branch, Borujerd, Iran.)
A.  Shahsavaran ² (Department of Mathematics, Islamic Azad University, Borujerd Branch, Borujerd, Iran.)

Received: 2015-09-28 Accepted : 2015-09-28 Published : 2013-12-01

Keywords:

Abstract :

In this work, we present a numerical method for solving nonlinear Fredholmand Volterra integral equations of the second kind which is based on the useof Block Pulse functions(BPfs) and collocation method. Numerical examplesshow eciency of the method.

References:

[1] K. E. Atkinson, The numerical solution of integral equations of the second
kind, Cambridge University Press, 1997.
[2] K. E. Atkinson, A survey of numerical methods for solving nonlinear
integral equations, J. Integral Equations Appl. 4 (1992) 15{46.
[3] E. Babolian, Z. Masouri, S. H. Varmazyar, Introdusing a direct method to
solve nonlinear Volterra and Fredholm integral equations using orthogonal
triangular functions, Math. Sci. J., 5 (2009) 11{26.
[4] M. Ghasemi, M. T. Kajani, A. Azizi, The application of homotopy
perturbation method for solving Schrodinger equation, Math. Sci. J., 5
(2009) 47{55.
[5] J. Kondo, Integral equations, Oxford University Press, 1991.

[6] K. Maleknejad, M. Hadizadeh, Algebraic nonlinearity in Volterra-
Hammerstein equations, J. Sci. I. R. Iran, 10 (1999).
[7] K. Maleknejad, M. Karami, N. Aghazadeh, Numerical solution of
Hammerstein equations via an interpolation method, Applied Mathematics
and Compution 168 (2005) 141{145.
[8] K. Maleknejad, M. Karami, Numerical solution of nonlinear Fredholm
integral equations by using multiwavelets in the Petrov-Galerkin method,
Appl. Math. Comput. 168 (2005) 102{110.
[9] N. Parandin, Numerical solution of linear and nonlinear Fredholm integral
equation of the second kind using nite dierences method, Math. Sci. J.,
5 (2009) 113{122.
[10] A. Shahsavaran, E. Babolian, Computational method for solving nonlinear
Fredholm integral equations of Hammerstein type based on Lagrange
interpolation and quadrature method, Math. Sci. J., 5 (2009) 137{145.
[11] T. Cardinali, N. S. Papageorgiou, Hammerstein integral inclusions in
re exive banach spaces, Amer. Math. Soc. 127 (1999) 95{103.