Numerical Solution of Functional Volterra–Hammerstein Integro-differential Equations of Order Two

  • L. Saeedi
  • A. TariEmail author
  • E. Babolian
Research Paper
Part of the following topical collections:
  1. Mathematics


In this paper, the functional Volterra–Hammerstein integro-differential equations (FVHIDEs) of order two with variable coefficients are studied. First, the existence and uniqueness of the solution to the mentioned problem are proved. Then a numerical method is proposed to solve the FVHIDEs. The proposed method is a combination of the well-known finite difference method with successive approximations method, trapezoidal quadrature rule and natural cubic spline interpolation method. An error bound is obtained, and the convergence of the method is proved. The numerical stability of the method is also proved by a suitable way. Finally, some examples are given to show the accuracy and efficiency of the proposed method.


Volterra–Hammerstein integro-differential equations Successive approximations Finite difference Spline interpolation Trapezoidal quadrature rule 

Mathematics Subject Classification

65R20 97N40 



The authors would like to thank the anonymous referees for their valuable comments that helped the authors to improve the paper.


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Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of MathematicsShahed UniversityTehranIran
  2. 2.Department of Computer ScienceKharazmi UniversityTehranIran

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