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Modified decomposition method for nonlinear Volterra–Fredholm integral equations

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  • Bildik, Necdet
  • Inc, Mustafa

Abstract

In this paper, the nonlinear Volterra–Fredholm integral equations are solved by using the modified decomposition method (MDM). The approximate solution of this equation is calculated in the form of a series with easily computable components. The accuracy of the proposed numerical scheme is examined by comparison with other analytical and numerical results. Two test problems are presented to illustrate the reliability and the performance of the modified decomposition method.

Suggested Citation

  • Bildik, Necdet & Inc, Mustafa, 2007. "Modified decomposition method for nonlinear Volterra–Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 308-313.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:1:p:308-313
    DOI: 10.1016/j.chaos.2005.12.058
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    Cited by:

    1. Ramos, J.I., 2009. "Piecewise-adaptive decomposition methods," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1623-1636.
    2. Chen, Zhong & Jiang, Wei, 2015. "An efficient algorithm for solving nonlinear Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 614-619.
    3. Golbabai, A. & Keramati, B., 2008. "Easy computational approach to solution of system of linear Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 568-574.
    4. Ramos, J.I., 2009. "Generalized decomposition methods for nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1078-1084.
    5. Dehghan, Mehdi & Shakourifar, Mohammad & Hamidi, Asgar, 2009. "The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2509-2521.
    6. Beiglo, H. & Gachpazan, M., 2020. "Numerical solution of nonlinear mixed Volterra-Fredholm integral equations in complex plane via PQWs," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    7. Alan Jalal Abdulqader, 2018. "Numerical Solution for Solving System of Fuzzy Nonlinear Integral Equation by Using Modified Decomposition Method," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(1), pages 32-43, February.

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