Shamivand, M., Shahsavaran, A. (2011). Numerical solution of Hammerstein Fredholm and Volterra integral equations of the second kind using block pulse functions and collocation method. Theory of Approximation and Applications, 7(2), 93-103.

M. M. Shamivand; A. Shahsavaran. "Numerical solution of Hammerstein Fredholm and Volterra integral equations of the second kind using block pulse functions and collocation method". Theory of Approximation and Applications, 7, 2, 2011, 93-103.

Shamivand, M., Shahsavaran, A. (2011). 'Numerical solution of Hammerstein Fredholm and Volterra integral equations of the second kind using block pulse functions and collocation method', Theory of Approximation and Applications, 7(2), pp. 93-103.

Shamivand, M., Shahsavaran, A. Numerical solution of Hammerstein Fredholm and Volterra integral equations of the second kind using block pulse functions and collocation method. Theory of Approximation and Applications, 2011; 7(2): 93-103.

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

^{}Department of Mathematics, Islamic Azad University, Borujerd Branch, Borujerd, Iran.

Abstract

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

Article Title [Persian]

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

Authors [Persian]

M. M. Shamivand; A. Shahsavaran

^{}Department of Mathematics, Islamic Azad University, Borujerd Branch,
Borujerd, Iran.

Abstract [Persian]

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

Keywords [Persian]

Hammerstein Fredholm and Volterra integral equations، Block
Pulse functions، collocation 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.