1 Karaj Branch, Islamic Azad University Iran, Islamic Republic of

2 Iran, Islamic Republic of


In this paper, we introduce an efficient method based on Haar wavelet to approximate a solution
for the two-dimensional linear stochastic Fredholm integral equation. We also give an example to demonstrate the accuracy of the method.


I. Aziz, Siraj-ul-Islam, F. Khan, A new method based on Haar wavelet for numerical solution of two-dimensional nonlinear integral equations, J. Comp. Appl. Math. 272 (2014), 70-80.

I. Aziz, Siraj-ul-Islam, New algorithms for numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets, J. Comp. Appl. Math. 239 (2013) 333-345.

Siraj-ul-Islam, I. Aziz, M. Fayyaz, A new approach for numerical solution of integro-differential equations via Haar wavelets, Int, J. Comp. Math. 90 (2013) 1971-1989.

Siraj-ul-Islam, I. Aziz, A. Al-Fhaid, An improved method based on Haar wavelets for numerical solution of nonlinear and integro-differential equations of rst and higher orders, J. Comp. Appl. Math. 260 (2014) 449-469.

Kuo, Hui-Hsiung, Introduction to stochastic integration, Springer Science+Business Media, Inc. 2006.

K. E. Atkinson, The numerical solution of integral equations of the second kind, Cambridge University Press (1997).

A. J. Jerri, Introduction to integral equations with applications, John Wiley and Sons, INC (1999).

T. S. Sankar, V. I. Fabrikant, Investigations of a two-dimentional integral equation in the theory of elasticity and electrostatics, J. Mec. Theor. Appl. 2 (1983) 285-299.

H. J. Dobner, Bounds for the solution of hyperbolic problems, Computing 38 (1987) 209-218.

V. M. Aleksandrov, A. V. Manzhirov, Two-dimentional integral equations in applied mechanics of deformable solids, J. Appl. Mech. Tech. Phys. 5 (1987) 146-152.

A. V. Manzhirov, Contact problems of the interaction between viscoelastic foundations subject to ageing and systems of stamps not applied simultaneously, Prikl. Matem. Mekhan. 4 (1987) 523-535.

O. V. Soloviev, Low-frequency radio wave propagation in the earth-ionosphere waveguide disturbed by a large-scale three-dimensional irregularity, Radiophysics and Quantum Electronics 41 (1998) 392-402.

M. Rahman, "A rigid elliptical disc-inclusion in an elastic solid", subject to a polynomial normal shift, J. Elasticity 66 (2002) 207-235.

H. Guoqiang, W. Jiong, Extrapolation of nystrom solution for two dimentional nonlinear Fredholm integral equations, J. Comp. App. Math. 134 (2001) 259-268.

H. Brunner, Collocation methods for Volterra integral and related functional equations, Cambridge University Press, 2004.

H. Guoqiang, K. Itayami, K. Sugihara, W. Jiong, Extrapolation method of iterated collocation solution for two-dimentional nonlinear Volterra integral equations, Appl. Math. Comput. 112 (2000) 49-61.

W. Xie, F. R. Lin, A fast numerical solution method for two dimensional Fredholm integral equations of the second kind, App. Num. Math. 59 (2009) 1709-1719.

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

G. Han, R. Wang, Richardson extrapolation of iterated discrete Galerkin solution for two dimensional Fredholm integral equations, J. Comp. App. Math. 139 (2002) 49-63.

K. Maleknejad, Z. JafariBehbahani, Application of two-dimensional triangular functions for solving nonlinear class of mixed Volterra-Fredholm integral equations, Math. Comp. Mode. 55(2012) 1833-1844.

E. Babolian, K. Maleknejad, M. Roodaki, H. Almasieh, Two dimensional triangular functions and their applications to nonlinear 2d Volterra-Fredholm equations, Comp. Math. App. 60 (2010) 1711-1722.

S. Nemati, P. Lima, Y. Ordokhani, Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using legender polynomials, J. Comp. Appl. Math. 242 (2013) 53-69.

A. Tari, M. Rahimi, S. Shahmorad, F. Talati, Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method, J. Comp. Appl. Math. 228 (2009) 70-76.

P. Assari, H. Adibi, M. Dehghal, A meshless method for solving nonlinear two-dimensional integral equations of the second kind on non-rectangular domains using radial basis functions with error analysis, J. Comp. Appl. Math. 239 (2013) 72-92.

M. H. Reihani, Z. Abadi, Rationalized Haar functions method for solving Fredholm and Volterra integral equations, J. Comp. Appl. Math. 200 (2007) 12-20.

F. Hosseini Shekarabi, K. Maleknejad, R. Ezzati, Application of two-dimensional Bernstein polynomials for solving mixed Volterra-Fredholm integral equations, African Mathematical Union and Springer-Verlag Berlin Heidelberg, DOI 10. 1007/s 13370-014-0283-6 2014.

F. Keinert, Wavelets and Multiwavelets, A Crc Press Company Boca Raton London New York Washington, D. C, 2004.