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Application of Reproducing Kernel Hilbert Space Method for Solving a Class of Nonlinear Integral Equations

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  • Sedigheh Farzaneh Javan
  • Saeid Abbasbandy
  • M. Ali Fariborzi Araghi

Abstract

A new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second-kind nonlinear integral equations. In this case, the Gram-Schmidt process is substituted by another process so that a satisfactory result is obtained. In this method, the solution is expressed in the form of a series. Furthermore, the convergence of the proposed technique is proved. In order to illustrate the effectiveness and efficiency of the method, four sample integral equations arising in electromagnetics are solved via the given algorithm.

Suggested Citation

  • Sedigheh Farzaneh Javan & Saeid Abbasbandy & M. Ali Fariborzi Araghi, 2017. "Application of Reproducing Kernel Hilbert Space Method for Solving a Class of Nonlinear Integral Equations," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-10, March.
    • Handle: RePEc:hin:jnlmpe:7498136
    DOI: 10.1155/2017/7498136
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    Cited by:

    1. Chen, Shu-Bo & Soradi-Zeid, Samaneh & Dutta, Hemen & Mesrizadeh, Mehdi & Jahanshahi, Hadi & Chu, Yu-Ming, 2021. "Reproducing kernel Hilbert space method for nonlinear second order singularly perturbed boundary value problems with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Ali Akgül & Esra Karatas Akgül & Dumitru Baleanu & Mustafa Inc, 2018. "New Numerical Method for Solving Tenth Order Boundary Value Problems," Mathematics, MDPI, vol. 6(11), pages 1-9, November.

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