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Multi-Wavelets Galerkin Method for Solving the System of Volterra Integral Equations

Author

Listed:
  • Hoang Viet Long

    (Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam
    Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam)

  • Haifa Bin Jebreen

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Stefania Tomasiello

    (Institute of Computer Science, University of Tartu, 50090 Tartu, Estonia)

Abstract

In this work, an efficient algorithm is proposed for solving the system of Volterra integral equations based on wavelet Galerkin method. This problem is reduced to a set of algebraic equations using the operational matrix of integration and wavelet transform matrix. For linear type, the computational effort decreases by thresholding. The convergence analysis of the proposed scheme has been investigated and it is shown that its convergence is of order O ( 2 − J r ) , where J is the refinement level and r is the multiplicity of multi-wavelets. Several numerical tests are provided to illustrate the ability and efficiency of the method.

Suggested Citation

  • Hoang Viet Long & Haifa Bin Jebreen & Stefania Tomasiello, 2020. "Multi-Wavelets Galerkin Method for Solving the System of Volterra Integral Equations," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1369-:d:399560
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    References listed on IDEAS

    as
    1. Biazar, J. & Ghazvini, H., 2009. "He’s homotopy perturbation method for solving systems of Volterra integral equations of the second kind," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 770-777.
    2. Seyedi, S.H. & Saray, B.N. & Nobari, M.R.H., 2015. "Using interpolation scaling functions based on Galerkin method for solving non-Newtonian fluid flow between two vertical flat plates," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 488-496.
    3. Adem Kılıçman & L. Kargaran Dehkordi & M. Tavassoli Kajani, 2012. "Numerical Solution of Nonlinear Volterra Integral Equations System Using Simpson’s 3/8 Rule," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-16, September.
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