The aim of this research is to apply the stochastic arithmetic (SA) for validating the Sinc-collocation method (S-CM) with single or double exponentially decay to find the numerical solution of second kind Fredholm integral equation (IE). To this end, the CESTAC(Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library are applied. Using this method, the optimal iteration of S-CM, the optimal approximation, the absolute error and the numerical instabilities can be determined. A theorem is proved which shows the accuracy of the S-CM by means of the concept of common significant digits. Some IEs are presented and the numerical results of comparison between the single exponentially decay (SE) and the double exponentially decay (DE) are demonstrated in the tables.
Fariborzi, M. A., & Noeiaghdam, S. (2019). Valid implementation of the Sinc-collocation method to solve linear integral equations by the CADNA library. Journal of Mathematical Modeling, 7(1), 63-84. doi: 10.22124/jmm.2018.11608.1200
MLA
Mohammad Ali Fariborzi; Samad Noeiaghdam. "Valid implementation of the Sinc-collocation method to solve linear integral equations by the CADNA library". Journal of Mathematical Modeling, 7, 1, 2019, 63-84. doi: 10.22124/jmm.2018.11608.1200
HARVARD
Fariborzi, M. A., Noeiaghdam, S. (2019). 'Valid implementation of the Sinc-collocation method to solve linear integral equations by the CADNA library', Journal of Mathematical Modeling, 7(1), pp. 63-84. doi: 10.22124/jmm.2018.11608.1200
VANCOUVER
Fariborzi, M. A., Noeiaghdam, S. Valid implementation of the Sinc-collocation method to solve linear integral equations by the CADNA library. Journal of Mathematical Modeling, 2019; 7(1): 63-84. doi: 10.22124/jmm.2018.11608.1200
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