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Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system

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  • Sahu, P.K.
  • Ray, S.Saha

Abstract

In this paper, Legendre wavelet method is developed to approximate the solutions of system of nonlinear Volterra integro-differential equations. The properties of Legendre wavelets are first presented. The properties of Legendre wavelets are used to reduce the system of integral equations to a system of algebraic equations which can be solved numerically by Newton’s method. Also, the results obtained by present method have been compared with that of by B-spline wavelet method. Illustrative examples have been discussed to demonstrate the validity and applicability of the present method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:715-723
    DOI: 10.1016/j.amc.2015.01.063
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    References listed on IDEAS

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    1. 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.
    2. Biazar, J. & Ghazvini, H. & Eslami, M., 2009. "He’s homotopy perturbation method for systems of integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1253-1258.
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    Cited by:

    1. Sahu, P.K. & Saha Ray, S., 2015. "Legendre spectral collocation method for Fredholm integro-differential-difference equation with variable coefficients and mixed conditions," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 575-580.
    2. Muhammed I. Syam & Mohammed Abu Omar, 2018. "A Numerical Method for Solving a Class of Nonlinear Second Order Fractional Volterra Integro-Differntial Type of Singularly Perturbed Problems," Mathematics, MDPI, vol. 6(4), pages 1-22, March.

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