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2 Journal of Applied Mathematics and Computational Mechanics

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Numerical approximation of the Riemann-Liouville fractional integrals using the akima spline interpolation

Grodzki Grzegorz

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 4

30-43

This paper presents the numerical algorithms for evaluating the values of the left- and right-sided Riemann-Liouville fractional integrals using the linear and Akima cubic spline interpolations. Sample numerical calculations have been performed based on the derived algorithms. The results are presented in two tables. Knowledge of the closed analytical expressions for sample fractional integrals makes it possible to determine the numerical errors and the experimental rates of convergence for each derived algorithm.

Strategic analysis of implementation assets and threats

Piech Henryk, Grodzki Grzegorz

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 2

65--74

The main goal of the work is to support the marketing strategy using the characteristics created on the base of the game theory and uncertain knowledge. We want to elaborate algorithm, which does not require game-playing investigation. The additional aim consists in adaptating the game strategy to the concrete e.g. economic situation, described by selected, specific parameters. The next aim consists in exploitation uncertain knowledge as a data also. Game theory is the part of mathematics approach extended by Nash and adopted to psychology, sociology, politics, economics and informatics (artificial intelligence) problems. Game Theory provides mathematical tools for analyzing situations in which parties, called players, make decisions that are interdependent. This causes each player to consider the other player’s possible decisions, or strategies, in formulating his own strategy. This approach based on the assumption, that a solution to a game describes the optimal decisions of the players, who may have similar, opposed, or mixed interests, and the outcomes that may result from these decisions. This will be described as an example.