فهرس المقالات Fuzzy integral equations

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  1 - Solving Fuzzy Integral Equations of the Second Kind by using the Reproducing Kernel Hilbert Space Method
  صدیقه فرزانه جوان سعید عباسبندی محمدعلی فریبرزی عراقی
  In this study, a new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second kind fuzzy linear integral equations. For this purpose, at first by applying the concept of parametric form, the fuzzy integral equat أکثر

  In this study, a new approach based on the Reproducing Kernel Hilbert Space Method is proposed to approximate the solution of the second kind fuzzy linear integral equations. For this purpose, at first by applying the concept of parametric form, the fuzzy integral equation is converted to a system of crisp integral equations. Then, this system is solved by using the reproducing kernel method free of the Gram-Schmidt orthogonalization process. Also, two numerical algorithms are proposed based on applying the Gram-Schmidt process and without using it. The general form of numerical solution accordingly the reproducing kernel method is introduced and the convergence theorem of solution of the proposed scheme to the exact solution is proved. Finally, a sample fuzzy integral equation is solved by means of both suggested algorithms and the results are compared for differents points and levels. Due to the difficulties in applying the Gram-Schmidt process, the obtained results of the new algorithm are satisfactory. تفاصيل المقالة
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  2 - On Optimal Quadrature Rule for Solving Fuzzy Fredholm Integral Equations
  R. Ezzati M. M. Sadatrasou
  In this paper, we present an efficient iterative procedure based on optimal fuzzy quadrature formula to solve fuzzy integral equations. Error estimation and the numerical stability analysis with respect to the choice of the first iteration are given. Some illustrative a أکثر

  In this paper, we present an efficient iterative procedure based on optimal fuzzy quadrature formula to solve fuzzy integral equations. Error estimation and the numerical stability analysis with respect to the choice of the first iteration are given. Some illustrative and comparative numerical experiments confirm the optimization of the successive ‎method.‎ تفاصيل المقالة
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  3 - Solving linear and nonlinear Volterra Fuzzy Integral Equations System via Differential Transform Method
  Mahmoud Paripour Mandana Takrimi
  10.30495/fomj.2022.1950726.1058
  In this study, we consider solving the second kind Volterra fuzzy integral equations system in two cases linear and nonlinear by using a semi-analytic method, called Differential Transform Method (DTM). In this algorithm the first, we convert a Volterra fuzzy integral e أکثر

  In this study, we consider solving the second kind Volterra fuzzy integral equations system in two cases linear and nonlinear by using a semi-analytic method, called Differential Transform Method (DTM). In this algorithm the first, we convert a Volterra fuzzy integral equations system into two crisp integral equations systems of Volterra; then we solve each of them via DTM. If the equation has a solution in terms of the series expansion of known functions; this powerful method will catch the exact solution. Moreover, the ability and efficiency of the algorithm are shown by solving some numerical examples.In this study, we consider solving the second kind Volterra fuzzy integral equations system in two cases linear and nonlinear by using a semi-analytic method, called Differential Transform Method (DTM). In this algorithm the first, we convert a Volterra fuzzy integral equations system into two crisp integral equations systems of Volterra; then we solve each of them via DTM. If the equation has a solution in terms of the series expansion of known functions; this powerful method will catch the exact solution. Moreover, the ability and efficiency of the algorithm are shown by solving some numerical examples. تفاصيل المقالة