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Legendre wavelets method for the nonlinear Volterra–Fredholm integral equations

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  • Yousefi, S.
  • Razzaghi, M.

Abstract

A numerical method for solving the nonlinear Volterra–Fredholm integral equations is presented. The method is based upon Legendre wavelet approximations. The properties of Legendre wavelet are first presented. These properties together with the Gaussian integration method are then utilized to reduce the Volterra–Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Suggested Citation

  • Yousefi, S. & Razzaghi, M., 2005. "Legendre wavelets method for the nonlinear Volterra–Fredholm integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(1), pages 1-8.
    • Handle: RePEc:eee:matcom:v:70:y:2005:i:1:p:1-8
    DOI: 10.1016/j.matcom.2005.02.035
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    References listed on IDEAS

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    1. Razzaghi, M. & Yousefi, S., 2000. "Legendre wavelets direct method for variational problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(3), pages 185-192.
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    Cited by:

    1. 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.
    2. 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).
    3. Parand, K. & Aghaei, A.A. & Jani, M. & Ghodsi, A., 2021. "A new approach to the numerical solution of Fredholm integral equations using least squares-support vector regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 114-128.
    4. Balcı, Mehmet Ali & Sezer, Mehmet, 2016. "Hybrid Euler–Taylor matrix method for solving of generalized linear Fredholm integro-differential difference equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 33-41.
    5. Reema Gupta & Snehashish Chakraverty, 2024. "Pseudo-Spectral Galerkin Method Using Shifted Vieta-Fibonacci Polynomials for Stochastic Models: Existence, Stability, and Numerical Validation," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-20, December.
    6. Mirzaee, Farshid & Hoseini, Seyede Fatemeh, 2016. "Application of Fibonacci collocation method for solving Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 637-644.
    7. Amiri, Sadegh & Hajipour, Mojtaba & Baleanu, Dumitru, 2020. "A spectral collocation method with piecewise trigonometric basis functions for nonlinear Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    8. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    9. Erfanian, Majid & Mansoori, Amin, 2019. "Solving the nonlinear integro-differential equation in complex plane with rationalized Haar wavelet," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 223-237.
    10. Mirzaee, Farshid & Hadadiyan, Elham, 2016. "Numerical solution of Volterra–Fredholm integral equations via modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 110-123.
    11. Sahu, P.K. & Ray, S.Saha, 2015. "Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 715-723.

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