10.1186/2251-7456-7-3

Solving nonlinear two-dimensional Volterra integro-differential equations by block-pulse functions

HTML PDF
  • Nasser Aghazadeh*1,
  • Amir Ahmad Khajehnasiri2,
  1. Research Group of Processing and Communication and Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, 53751 71379, IR
  2. Department of Mathematics, Payame Noor University, Tabriz, 51746 78161, IR

Published in Issue 2013-01-16

How to Cite

Aghazadeh, N., & Khajehnasiri, A. A. (2013). Solving nonlinear two-dimensional Volterra integro-differential equations by block-pulse functions. Mathematical Sciences, 7(1). https://doi.org/10.1186/2251-7456-7-3
Crossref
Scopus
Google Scholar
Europe PMC

HTML views: 17

PDF views: 87

Abstract

Abstract In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions. First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Volterra integro-differential equation has been reduced to an algebraic system. Some numerical examples are presented to illustrate the effectiveness and accuracy of the method.

Keywords

  • Nonlinear equations,
  • Two-dimensional Volterra integro-differential equations,
  • Two-dimensional block-pulse functions,
  • Operational matrix
HTML PDF

References

  1. Darania et al. (2011) New computational method for solving some 2-dimensional nonlinear Volterra integro-differential equations (pp. 125-147) https://doi.org/10.1007/s11075-010-9419-4
  2. Jerry (1999) Wiley
  3. Kress (1989) Springer https://doi.org/10.1007/978-3-642-97146-4
  4. Tari et al. (2009) Development of the tau method for the numerical solution of two-dimensional linear Volterra integro-differential equations (pp. 421-435) https://doi.org/10.2478/cmam-2009-0027
  5. Brunner (2004) Cambridge University Press https://doi.org/10.1017/CBO9780511543234
  6. Harmuth (1969) Springer https://doi.org/10.1007/978-3-662-13227-2
  7. Kung and Chen (1978) Solution of integral equations using a set of block pulse functions (pp. 283-291) https://doi.org/10.1016/0016-0032(78)90037-6
  8. Maleknejad and Mahmoudi (2004) Numerical solution of linear Fredholm integral equation by using hybrid Taylor and block–pulse functions (pp. 799-806) https://doi.org/10.1016/S0096-3003(03)00180-2
  9. Marzban et al. (2009) Solution of Volterra’s population model via block-pulse functions and Lagrange-interpolating polynomials (pp. 127-134) https://doi.org/10.1002/mma.1028
  10. Maleknejad and Mahdiani (2011) Solving nonlinear mixed Volterra-Fredholm integral equations with the two dimensional block-pulse functions using direct method (pp. 3512-3519) https://doi.org/10.1016/j.cnsns.2010.12.036
  11. Maleknejad et al. (2010) Application of 2D-BPFs to nonlinear integral equations (pp. 527-535) https://doi.org/10.1016/j.cnsns.2009.04.011