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Sahand Communications in Mathematical Analysis، جلد ۲۲، شماره ۱، صفحات ۲۳۳-۲۵۸
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عنوان انگلیسی Euler Operational Matrix of Integration and Collocation Method for Solving Functional Integral Equations
چکیده انگلیسی مقاله 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.
کلیدواژه‌های انگلیسی مقاله Functional integral equations,Hammerstein integral equations,Collocation method,Euler polynomials,Operational matrix
نویسندگان مقاله Sohrab Bazm |
Department of Mathematics, Faculty of Science, University of Maragheh, 55136-553 Maragheh, Iran.

Fatemeh Pahlevani |
Department of Mathematics, Faculty of Science, University of Maragheh, 55136-553 Maragheh, Iran.

نشانی اینترنتی https://scma.maragheh.ac.ir/article_719397_0f8d47c010a041c7952add234a1a8a4c.pdf
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