2021
DOI: 10.3390/math9030260
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Abstract: The aim of this paper is to present a new method and the tool to validate the numerical results of the Volterra integral equation with discontinuous kernels in linear and non-linear forms obtained from the Adomian decomposition method. Because of disadvantages of the traditional absolute error to show the accuracy of the mathematical methods which is based on the floating point arithmetic, we apply the stochastic arithmetic and new condition to study the efficiency of the method which is based on two successiv… Show more

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Cited by 37 publications
(8 citation statements)
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References 43 publications
(54 reference statements)
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“…Recently, we focused on validating the numerical results of various problems using the CESTAC method. In [36], the results of the Adomian decomposition method for solving Volterra integral equation with a discontinuous kernel was studied and in [37,38] the CESTAC method was used to validate the results on the reverse osmosis system. Dynamical control on the homotopy perturbation method and the Taylor-collocation method to solve Volterra integral equations with piecewise smooth kernels was discussed in [39,40].…”
Section: Introductionmentioning
confidence: 99%
“…Recently, we focused on validating the numerical results of various problems using the CESTAC method. In [36], the results of the Adomian decomposition method for solving Volterra integral equation with a discontinuous kernel was studied and in [37,38] the CESTAC method was used to validate the results on the reverse osmosis system. Dynamical control on the homotopy perturbation method and the Taylor-collocation method to solve Volterra integral equations with piecewise smooth kernels was discussed in [39,40].…”
Section: Introductionmentioning
confidence: 99%
“…Thereafter, Waleed Al Hayani [32] and Singh et al [33] applied ADM with Green's function to compute the approximate solution. Recently, Noeiaghdam et al [34] proposed a technique based on ADM for solving Volterra integral equation with discontinuous kernels using the CESTAC method. To find out more about this method, please see [35,36].…”
Section: Introductionmentioning
confidence: 99%
“…In this theorem, we will show that the number of common significant digits for two successive approximations is almost equal to the number of common significant digits for exact and approximate solutions [21]. Recently, this method has been applied to validate the results of some numerical methods to solve the mathematical and engineering problems such as numerical integration rules [30,31], homotopy analysis method [32][33][34], homotopy perturbation method [35], Adomian decomposition method [36], collocation method [37][38][39], solving fuzzy problems [37,40,41], load leveling problem [42], reverse osmosis model [43] and many others [44]. For more information about the DSA, the CESTAC method and the CADNA library please see [21].…”
Section: Introductionmentioning
confidence: 99%