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Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

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  • Zakieh Avazzadeh
  • Mohammad Heydari
  • Wen Chen
  • G. B. Loghmani

Abstract

We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra‐Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill‐posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.

Suggested Citation

  • Zakieh Avazzadeh & Mohammad Heydari & Wen Chen & G. B. Loghmani, 2014. "Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:710437
    DOI: 10.1155/2014/710437
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    References listed on IDEAS

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    1. Abbasbandy, S., 2007. "Application of He’s homotopy perturbation method to functional integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1243-1247.
    2. Yildirim, Ahmet, 2009. "Homotopy perturbation method for the mixed Volterra–Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2760-2764.
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