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Mathematical modeling of many natural and physical phenomena in industry, engineering sciences and basic sciences lead to linear and non-linear devices. In many cases, the coefficients of these devices, taking into account qualitative or linguistic concepts, show their complexity in the form of Z-numbers. Since Z-number involves both fuzziness and reliability or probabilistic uncertainty, it is difficult to obtain the exact solution to the problems with Z-number. In this work, a method and an algorithm are proposed for the approximate solution of a Z-number linear system of equations as an important case of such problems. The paper is devoted to solving linear systems where the coefficients of the variables and right hand side values are Z-numbers. An algorithm is presented based on a ranking scheme and the neural network technique to solve the obtained system. Moreover, two examples are included to describe the procedure of the method and results. [ABSTRACT FROM AUTHOR]

An efficient family of the recursive methods of adaptive is proposed for solving nonlinear equations and is developed such that all previous information is applied. These methods have reached the maximum degree of convergence improvement of 100% and also have an efficiency index of 2. Three families have been examined from Steffensen-Like single, two, and three-step methods that have used 2, 3 and 4 parameters, respectively. Numerical comparisons have made with other existing methods one-, two-, three-, and four-point to show the performance of the convergence speed of the proposed method and confirm theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, using the modified Adomian decomposition method, a novel fast scheme, has been presented, being interactive, to be used for solving a class of hypersingular integral equations of the first kind. Compared to the standard Adomian decomposition method, this method expedites the quick accumulation of a series of solutions. Different problems, for exemplification, have been solved in order to display the accuracy and validity of the aforementioned method. According to the results, it gets known that the novel fast modified Adomian decomposition method is so efficient and simple which gives the exact solution, and also shuns the complicated function of long theoretical calculations of collocation methods based on polynomial producing the exact solution. [ABSTRACT FROM AUTHOR]

In this paper, a generalized Fisher's equation is solved by using the modified Adomian decomposition method (MADM), variational iteration method (VIM), homotopy analysis method (HAM). The approximation solution of this equation is calculated in the form of series in which its components are easily computed. The existence, uniqueness and convergence of the proposed methods are proved. Numerical example is studied to demonstrate the accuracy of the present methods. [ABSTRACT FROM AUTHOR]