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A Efficient Computational Method for Solving Stochastic Itô-Volterra Integral Equations

Yıl 2015, Cilt: 5 Sayı: 2, 286 - 297, 01.12.2015

Öz

In this paper, a new stochastic operational matrix for the Legendre wavelets is presented and a general procedure for forming this matrix is given. A computational method based on this stochastic operational matrix is proposed for solving stochastic It^o-Voltera integral equations. Convergence and error analysis of the Legendre wavelets basis are investigated. To reveal the accuracy and eciency of the proposed method some numerical examples are included.

Kaynakça

  • Kloeden, P. E. and Platen, E., (1992), Numerical Solution of Stochastic Differential Equations, Springer-Verlag. New York.
  • Oksendal, B., (2013), Stochastic differential equations: An introduction with applications, Springer Science and Business Media.
  • Maleknejad, K., Khodabin, M. and Rostami, M., (2012), Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions. Mathematical and Computer Modelling, 55(3), pp. 791-800.
  • Maleknejad, K., Khodabin, M. and Rostami, M., (2012), A numerical method for solving m- dimensional stochastic Itˆo-Volterra integral equations by stochastic operational matrix. Computers and Mathematics with Applications, 63(1), pp. 133-143.
  • Khodabin, M., Maleknojad, K. and Hossoini Shckarabi, F., (2013), Application of triangular func- tions to numerical solution of stochastic Volterra integral equations. IAENG International Journal of Applied Mathematics, 43(1), pp. 1-9.
  • Khodabin, M., Maleknejad, K., Rostami, M. and Nouri, M., (2012), Numerical approach for solving stochastic Volterra-Fredholm integral equations by stochastic operational matrix. Computers and Mathematics with Applications, 64(6), pp. 1903-1913.
  • Heydari, M. H., Hooshmandasl, M. R., Ghaini, F. M. and Cattani, C., (2014), A computational method for solving stochastic Itˆo-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions. Journal of Computational Physics, 270, pp. 402-415.
  • Cortes, J. C., Jodar, L. and Villafuerte, L., (2007), Numerical solution of random differential equations: a mean square approach. Mathematical and Computer Modelling, 45(7), pp. 757-765.
  • Cortes, J. C., Jodar, L. and Villafuerte, L., (2007), Mean square numerical solution of random differ- ential equations: Facts and possibilities. Computers and Mathematics with Applications, 53(7), pp. 1098-1106.
  • Jankovic, S. and Ilic, D., (2010), One linear analytic approximation for stochastic integrodifferential equations. Acta Mathematica Scientia, 30(4), pp. 1073-1085.
  • Strang, G., (1989), Wavelets and dilation equations: A brief introduction. SIAM review, 31(4), pp. 614-627.
  • Boggess, A. and Narcowich, F. J., (2009), A first course in wavelets with Fourier analysis. John Wiley and Sons.
  • Razzaghi, M. and Yousefi, S., (2001), The Legendre wavelets operational matrix of integration. Inter- national Journal of Systems Science, 32(4), pp. 495-502.
  • Razzaghi, M. and Yousefi, S., (2000), Legendre wavelets direct method for variational problems. Mathematics and Computers in Simulation, 53(3), pp. 185-192.
  • Mohammadi, F., Hosseini, M. M. and Mohyud-Din, S. T., (2011), Legendre wavelet galerkin method for solving ordinary differential equations with non-analytic solution. International Journal of Systems Science, 42(4), pp. 579-585.
  • Mohammadi, F. and Hosseini, M. M., (2011), A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations. Journal of the Franklin Institute, 348(8), pp. 1787-1796.
  • Jiang, Z., Schoufelberger, W., Thoma, M. and Wyner, A., (1992), Block pulse functions and their applications in control systems. Springer-Verlag New York, Inc.
  • Liu, N. and Lin, E. B., (2010), Legendre wavelet method for numerical solutions of partial differential equations. Numerical Methods for Partial Differential Equations, 26(1), pp. 81-94.
Yıl 2015, Cilt: 5 Sayı: 2, 286 - 297, 01.12.2015

Öz

Kaynakça

  • Kloeden, P. E. and Platen, E., (1992), Numerical Solution of Stochastic Differential Equations, Springer-Verlag. New York.
  • Oksendal, B., (2013), Stochastic differential equations: An introduction with applications, Springer Science and Business Media.
  • Maleknejad, K., Khodabin, M. and Rostami, M., (2012), Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions. Mathematical and Computer Modelling, 55(3), pp. 791-800.
  • Maleknejad, K., Khodabin, M. and Rostami, M., (2012), A numerical method for solving m- dimensional stochastic Itˆo-Volterra integral equations by stochastic operational matrix. Computers and Mathematics with Applications, 63(1), pp. 133-143.
  • Khodabin, M., Maleknojad, K. and Hossoini Shckarabi, F., (2013), Application of triangular func- tions to numerical solution of stochastic Volterra integral equations. IAENG International Journal of Applied Mathematics, 43(1), pp. 1-9.
  • Khodabin, M., Maleknejad, K., Rostami, M. and Nouri, M., (2012), Numerical approach for solving stochastic Volterra-Fredholm integral equations by stochastic operational matrix. Computers and Mathematics with Applications, 64(6), pp. 1903-1913.
  • Heydari, M. H., Hooshmandasl, M. R., Ghaini, F. M. and Cattani, C., (2014), A computational method for solving stochastic Itˆo-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions. Journal of Computational Physics, 270, pp. 402-415.
  • Cortes, J. C., Jodar, L. and Villafuerte, L., (2007), Numerical solution of random differential equations: a mean square approach. Mathematical and Computer Modelling, 45(7), pp. 757-765.
  • Cortes, J. C., Jodar, L. and Villafuerte, L., (2007), Mean square numerical solution of random differ- ential equations: Facts and possibilities. Computers and Mathematics with Applications, 53(7), pp. 1098-1106.
  • Jankovic, S. and Ilic, D., (2010), One linear analytic approximation for stochastic integrodifferential equations. Acta Mathematica Scientia, 30(4), pp. 1073-1085.
  • Strang, G., (1989), Wavelets and dilation equations: A brief introduction. SIAM review, 31(4), pp. 614-627.
  • Boggess, A. and Narcowich, F. J., (2009), A first course in wavelets with Fourier analysis. John Wiley and Sons.
  • Razzaghi, M. and Yousefi, S., (2001), The Legendre wavelets operational matrix of integration. Inter- national Journal of Systems Science, 32(4), pp. 495-502.
  • Razzaghi, M. and Yousefi, S., (2000), Legendre wavelets direct method for variational problems. Mathematics and Computers in Simulation, 53(3), pp. 185-192.
  • Mohammadi, F., Hosseini, M. M. and Mohyud-Din, S. T., (2011), Legendre wavelet galerkin method for solving ordinary differential equations with non-analytic solution. International Journal of Systems Science, 42(4), pp. 579-585.
  • Mohammadi, F. and Hosseini, M. M., (2011), A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations. Journal of the Franklin Institute, 348(8), pp. 1787-1796.
  • Jiang, Z., Schoufelberger, W., Thoma, M. and Wyner, A., (1992), Block pulse functions and their applications in control systems. Springer-Verlag New York, Inc.
  • Liu, N. and Lin, E. B., (2010), Legendre wavelet method for numerical solutions of partial differential equations. Numerical Methods for Partial Differential Equations, 26(1), pp. 81-94.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

F. Mohammadi Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 5 Sayı: 2

Kaynak Göster