Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations

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Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
In this paper, the functional Volterra integral equations of the Hammerstein type are studied. First, some conditions that ensure the existence and uniqueness of the solutions to these equations within the space of square-integrable functions are established and then the Euler operational matrix of integration is constructed and applied within the collocation method for approximating the solutions. This approach transforms the integral equation into a set of nonlinear algebraic equations, which can be efficiently solved by employing standard numerical methods like Newton's method or Picard iteration. One significant advantage of this method lies in its ability to avoid the need for direct integration to discretize the integral operator. Error estimates are provided and two illustrative examples are included to demonstrate the method’s effectiveness and practical applicability.
Language:
English
Published:
Sahand Communications in Mathematical Analysis, Volume:22 Issue: 1, Winter 2025
Pages:
233 to 258
https://www.magiran.com/p2805543  
سامانه نویسندگان
  • Sohrab Bazm
    Corresponding Author (1)
    Associate Professor Department of Mathematics, Faculty of Science, Maragheh, Iran, University of Maragheh, Maragha, Iran
    Bazm، Sohrab
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