Numerical solution for system of singular nonlinear Volterra integro-differential equations by Newton-Product method

Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews

“…Since the inception of the fuzzy set theory, Soliman and Mantawy [5] showed that five major strongly connected branches have been developed, including fuzzy mathematics, fuzzy logic and artificial intelligence, fuzzy systems, uncertainty and information, and fuzzy decision-making. Their subbranches have also been established; for example, fuzzy differential equations [6][7][8][9][10][11][12][13][14] and fuzzy integrodifferential equations [15][16][17][18][19][20][21][22] are of fuzzy mathematics while fuzzy-number ranking, the focus of this paper, is of fuzzy decision-making. Specifically, based on its feasible mathematical capacity for representing the imprecise information in practice, we have observed many successful cases spreading in disparate disciplines, such as robot selection [23], supplier selection [24], logistics center allocation [25], facility location determination [26], choosing mining methods [27], manufacturing process monitoring [1,2,[28][29][30][31], cutting force prediction [32], firm-environmental knowledge management [33,34], green supply-chain operation [35], and weapon procurement decision [36].…”

Boole approximation method with residual error function to solve linear Volterra integro-differential equations

“…For the numerical solution of integro-differential equation classes, the method based on the Bernoulli polynomial by Erdem Biçer et al [1,13], the method based on the Bessel polynomial by Yüzbaşı et al [11,28], the method based on the Laguerre polynomial by Baykuş Savaşaneril and Sezer [27] and the method based on the Dickson polynomial by Kürkçü [15] have been developed [14,[16][17][18][19][20][21][22][23][24]. In addition, the numerical methods such as Taylor collocation method [2], a multiscale Galerkin method [3], Bernstein polynomials method [4], Legendre collocation method [5], Euler wavelet method [6], Newton-Product method [7], homotopy-perturbation method [8], improved Bessel collocation method [9], Spectral collocation method [10], Hybrid Euler-Taylor matrix method [29] and Tau method [12] are included in the literature.…”