Numerical study of stochastic Volterra–Fredholm integral equations by using second kind Chebyshev wavelets

References

1 A. Boggess and F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, John Wiley & Sons, Hoboken, 2001. Suche in Google Scholar

2 C. Cattani, Harmonic wavelet approximation of random, fractal and high frequency signals, Telecommun. Syst. 43 (2010), 207–217. 10.1007/s11235-009-9208-3Suche in Google Scholar

3 J . C. Cortes, L. Jodar and L. Villafuerte, Numerical solution of random differential equations: A mean square approach, Math. Comput. Model. 45 (2007), 757–765. 10.1016/j.mcm.2006.07.017Suche in Google Scholar

4 M. H. Heydari, M. R. Hooshmandasl, F. M. Maalek and C. Cattani, A computational method for solving stochastic Itô–Volterra integral equations based on stochastic operational matrix for generalized hat basis functions, J. Comput. Phys. 270 (2014), 402–415. 10.1016/j.jcp.2014.03.064Suche in Google Scholar

5 D. J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Rev. 43 (2001), 3, 525–546. 10.1137/S0036144500378302Suche in Google Scholar

6 S. Jankovic and D. Ilic, One linear analytic approximation for stochastic integro-differential equations, Acta Math. Sci. 30 (2010), 1073–1085. 10.1016/S0252-9602(10)60104-XSuche in Google Scholar

7 Z. H. Jiang and W. Schaufelberger, Block Pulse Functions and Their Applications in Control Systems, Lecture Notes in Control and Inform. Sci. 179, Springer, Berlin, 1992. 10.1007/BFb0009162Suche in Google Scholar

8 M. Khodabin, K. Maleknejad and F. Hosseini Shekarabi, Application of triangular functions to numerical solution of stochastic Volterra integral equations, IAENG Int. J. Appl. Math. 43 (2011), 1, 1–9. Suche in Google Scholar

9 M. Khodabin, K. Maleknejad, M. Rostami and M. Nouri, Numerical approach for solving stochastic Volterra–Fredholm integral equations by stochastic operational matrix, Comput. Math. Appl. 64 (2012), 1903–1913. 10.1016/j.camwa.2012.03.042Suche in Google Scholar

10 P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992. 10.1007/978-3-662-12616-5Suche in Google Scholar

11 K. Maleknejad, M. Khodabin and M. Rostami, Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions, Math. Comput. Model. 55 (2012), 791–800. 10.1016/j.mcm.2011.08.053Suche in Google Scholar

12 J. C. Mason and D. C. Handscomb, Chebyshev Polynomials, CRC Press, Boca Raton, 2010. Suche in Google Scholar

13 F. Mohammadi and M. M. Hosseini, A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations, J. Franklin Inst. 348 (2011), 8, 1787–1796. 10.1016/j.jfranklin.2011.04.017Suche in Google Scholar

14 F. Mohammadi, M. M. Hosseini and S. T. Mohyud-Din, Legendre wavelet Galerkin method for solving ordinary differential equations with non-analytic solution, Int. J. Syst. Sci. 42 (2011), 2, 579–585. 10.1080/00207721003658194Suche in Google Scholar

15 M. G. Murge and B. G. Pachpatte, Succesive approximations for solutions of second order stochastic integro-differential equations of Itô type, Indian J. Pure Appl. Math. 21 (1990), 3, 260–274. Suche in Google Scholar

16 B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, 5th ed., Springer, New York, 1998. 10.1007/978-3-662-03620-4Suche in Google Scholar

17 G. Strang, Wavelets and dilation equations: A brief introduction, SIAM Rev. 31 (1989), 4, 614–627. 10.1137/1031128Suche in Google Scholar