10.71932/

Using Radial Basis Functions for Numerical Solving Two-Dimensional Voltrra Linear Functional Integral Equations

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  • Firouzdor1,
  • Reza Khaksari2,
  • Atousa Emady3,
  1. Young Researcher Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
  2. Department of Mathematics, Faculty of Science, Hamedan Branch, Islamic Azad University, Hamedan, Iran
  3. Department of Computer, Islamic Azad University, Najafabad, Esfahan, Iran

Published in Issue 12-07-2025

Copyright (c) 2025 Firouzdor, Reza Khaksari, Atousa Emady (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Firouzdor, R., Khaksari, R., & Emady, A. (2025). Using Radial Basis Functions for Numerical Solving Two-Dimensional Voltrra Linear Functional Integral Equations. International Journal of Mathematical Modelling & Computations, 10(01). https://doi.org/10.71932/
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Abstract

This article is an attempt to obtain the numerical solution of functional linear Voltrra two-dimensional integral equations using Radial Basis Function (RBF) interpolation which is based on linear composition of terms. By using RBF in functional integral equation, first a linear system ΓC = G will be achieved; then the coefficients vector is defined, and finally the target function will be approximated. In the end, the validity of the method is shown by a number of examples. 

Keywords

  • Functional linear Voltrra integral equations,
  • Radial basis function interpolation,
  • Gaussian functions
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References

  1. [1] Sh. S. Asari, M. Amirfakhrian and S. Chakraverty, Application of radial basis function in solving
  2. fuzzy integral equation, Neural Computing and Application, 31 (2019) 6373-6381.
  3. [2] Sh. S. Asari, R. Firouzdor and M. Amirfakhrian, Numerical solution of functional nonlinear Feredholm integral equations by using RBF interpolation, 46th Annual Iranian Mathematics Conference,
  4. 25-28 August 2015, Yazd University, 331-334.
  5. [3] M. D. Buhmann and C. A. Micchelli, Multiquadric interpolation improved, Computers & Mathematics with Applications, 24 (12) (1992) 2125.
  6. [4] C. de Boor, Multivariate piecewise polynomials, Acta Numerica, 2 (1993) 65-109.
  7. [5] R. Firouzdor and M. Amirfakhrian, Approximation of a fuzzy function by using radial basis functions
  8. interpolation, International Journal of Mathematical Modelling & Computations, 7 (3) (2017) 299-
  9. 307.
  10. [6] R.Firouzdor, Sh. S. Asari and M. Amirfakhrian, Application of radial basis function to approximateR. Firouzdor et al./ IJM2C, 10 - 01 (2020) 1-11. 11
  11. functional integral equations, Journal of Interpolation and Approximation in Scientific Computing,
  12. 2 (2016) 77-86.
  13. [7] R. Firouzdor, Sh. S. Asari and M. Amirfakhrian, Radial basis function network in the numerical solution of linear integro-differential equation, Apllication Mathematics and Computation, 188 (2007)
  14. 427-432.
  15. [8] R. Franke, Scattered data interpolation: tests of some methods, Mathematics of Computation, 38
  16. (157) (1982) 181-200.
  17. [9] R. L. Hardy, Multiquadratic equation of topography and other irregular surfaces, Journal of Geophysical Research, 76 (1971) 1905-1915.
  18. [10] R. L. Hardy, Theory and applications of the multiquadricbiharmonic method: 20 years of discovery,
  19. Computers & Mathematics with Applications, 19 (89) (1990) 163-208.
  20. [11] E. J. Kansa, Multiquadrics-A scattered data approximation scheme with applications to computational fluid-dynamics-I surface approximations and partial derivative estimates, Computers & Mathematics with Applications, 19 (8-9) (1990) 127-145.
  21. [12] E. J. Kansa, Multiquadrics-A scattered data approximation scheme with applications to computational fluid-dynamics-II solutions to parabolic, hyperbolic and elliptic partial differential equations,
  22. Computers & Mathematics with Applications, (1990) 147-161.
  23. [13] M. J. Lai and L. L. Schumaker, Spline functions on triangulations Cambridge University Press,
  24. Cambridge, (2007).
  25. [14] C. A. Micchelli, Interpolation of scattered data: Distance matrices and conditionally positive definite
  26. functions, Constructive Approximation, 2 (1986) 11-22.
  27. [15] R. B. Platte, How fast do radial basis function interpolants of analytic functions converge, IMA
  28. Journal of Numerical Analysis, 31 (2011) 1578-1597.
  29. [16] M.T. Rashed, Numerical solution of functional differential, integral and integro-differential equations, Applied Mathematics and Computation, 156 (2004) 485-492.
  30. [17] M. T. Rashed, An Expansion method to treat integral equations, Applied Mathematics and Computation, 135 (2003) 65-72.
  31. [18] M. Tatari, New interpolation of radial basis functionfor solving Burgers-Fisher equation, Numerical
  32. Methods for partial Differential Equations, 28 (2012) 248-262.
  33. [19] Hu. Wei, Adaptive multiscale meshfree method for solving the Schrodinger equation in quantum
  34. mechanics, University of California, (2011).
  35. [20] H. Wendland, Scattered Data Approximation, Cambridge University Press, Cambridge, (2005).

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