Şişman, Şeyma; Merdan, Mehmet

In this study, Laplace transformation, which is very important for solutions to initial value problems, is examined. To solve the initial value problem of a discrete-time equation, Laplace implements the conversion method. Here, Laplace transformation is used to obtain an approach to the solutions of random difference equations formed by randomizing components of deterministic difference equations. For random behavior of linear difference equations under random effects, uniform, geometric, binomial, Poisson, and Bernouilli distributions are used, and approximate expected value, variance, standard deviation, and confidence interval of equations obtained by Laplace transformation are calculated. The results were obtained through the Maple package program.

Ashyralyyev, Charyyar

In this paper, we study the approximation of reverse parabolic problem with integral boundary condition. The Rothe difference scheme for an approximate solution of reverse problem is discussed. We establish stability and coercive stability estimates for the solution of the Rothe difference scheme. In sequel, we investigate the first order of accuracy difference scheme for approximation of boundary value problem for multidimensional reverse parabolic equation and obtain stability estimates for its solution. Finally, we give numerical results together with an explanation on the realization in one- and two-dimensional test examples.

Şahin, Rıdvan; Küçük, Gökçe Dilek

Simplified neutrosophic set is a convenient tool proposed for dealing with complex problems; it is effective in providing more data for decision-making process. In this study, we develop a simplified neutrosophic ordered weighted distance operator which combines the neutrosophic distance measures and the ordered weighted average distance in the same formulation. It is a new handy aggregation operator that considers the situations where the input data are represented in simplified neutrosophic numbers, and it also contains diverse distance aggregation operators. Parameterized families of simplified neutrosophic ordered weighted distance operator are handled. Moreover, we establish a new neutrosophic group decision-making method based on the simplified neutrosophic ordered weighted distance operator, which has 2 extended approaches for determining the weights of decision makers and decision attributes in decision-making process, respectively. Finally, an illustrative example demonstrates the application of the proposed method. The effectiveness and advantages of the proposed method are shown by the comparative analysis with existing relative methods.