فهرس المقالات Newton-Cotes

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  1 - Error estimation of ‎f‎uzzy Newton-Cotes method for Integration of fuzzy functions‎
  N. Ahmady E. Ahmady
  Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding erro أکثر

  Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and fuzzy Simpson rule is accurate for polynomial of degree three. The accuracy of fuzzy Trapezoidal rule and fuzzy Simpson rule for integration of fuzzy functions are illustrated by two ‎examples.‎ تفاصيل المقالة
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  2 - SPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS
  Z. Mahmoodi J. Rashidinia E. Babolian
  The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the int أکثر

  The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented method is tested with four examples, and the errors in the solution are compared with the existing methods [1, 2, 3, 4] to verify the accuracy and convergent nature of proposed methods. The RMS errors in the solutions are tabulated in table 3 which shows that our method can be applied for large values of n, but the maximum n which has been used by the existing methods are only n = 10, moreover our method is accurate and stable for different values of n. تفاصيل المقالة
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  3 - SPLINE COLLOCATION FOR FREDHOLM AND VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
  Nehzat Ebrahimi Jalil Rashidinia
  A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the أکثر

  A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toillustrate the efficiency of the proposed method which shows that our method can be applied for largevalues of N. The results are compared with the results obtained by other methods to illustrate the accuracyand the implementation of our method. تفاصيل المقالة