Valid implementation of Sinc-collocation method to solve the fuzzy Fredholm integral equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:370

Article

Noeiaghdam, Samad^1,2,3  Araghi, Mohammad Ali Fariborzi¹  Abbasbandy, Saeid⁴ 

[1] Islamic Azad Univ, Dept Math, Cent Tehran Branch, Tehran 1955847881, Iran

[2] Irkutsk Natl Res Tech Univ, Baikal Sch BRICS, Irkutsk, Russia

[3] South Ural State Univ, Lenin Prospect 76, Chelyabinsk 454080, Russia

[4] Imam Khomeini Int Univ, Fac Sci, Dept Appl Math, Qazvin 3414916818, Iran

关键词: Discrete stochastic arithmetic (DSA);    Fuzzy CESTAC method;    CADNA library;    Sinc-collocation method;    Single (Double) exponential decay;    Fuzzy Fredholm integral equation;   

DOI  :  10.1016/j.cam.2019.112632

来源: Elsevier

【 摘 要 】

The main purpose of this work is to validate the numerical solution of fuzzy Fredholm integral equation (IE) by applying the Sinc-collocation method (S-CM) based on the double exponential (DE) and single exponential (SE) decays. This approach is based on the discrete stochastic arithmetic (DSA) which is able to validate the results with optimal solution and rely the proposed algorithm in comparison with the floating-point arithmetic (FPA). In order to achieve this goal, the fuzzy CESTAC(1) method and the CADNA(2) library are applied. The accuracy of the S-CM in both SE and DE cases is discussed by proving the theorems. Also, two numerical algorithms based on the S-CM in SE and DE decays by applying the fuzzy CESTAC method and CADNA library are presented. The termination criterion in each algorithm is based on the Hausdorff distance to be an informatical zero. By solving the examples, not only the optimal approximation and the optimal iteration of the S-CM can be found but also similar to the non-fuzzy case, it is shown that the DE precision is more accurate with faster convergence rate than the SE. (C) 2019 Published by Elsevier B.V.

【 授权许可】

Free