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

Abstract 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.

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