Квазіньютонівські методи для моделювання плоских кривих: Fìz.-mat. model. ìnf. tehnol. 2021, 33:62-67

• Datum: 2021
• Hauptverfasser: Nesterenko, Alla, Duchenko, Oleksandr
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Schlagworte: геометричне моделювання; плоска крива; S-подібна крива; лінійний (квадратичний) закон розподілу кривини; розв’язування системи нелінійних інтегральних рівнянь
• Online Zugang: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/203
• Назва журналу: Physico-mathematical modeling and informational technologies

The paper is devoted to the methods of geometric modeling of plane curves given in the natural parameterization. The paper considers numerical modeling methods that make it possible to find the equation of curvature of the desired curve for different cases of the input data. The unknown curvature distribution coefficients of the required curve are determined by solving a system of nonlinear integral equations. Various numerical methods are considered to solve this nonlinear system. The results of computer implementation of the proposed methods for modeling two curvilinear contours with different initial data are presented. For the first curve, the input data are the coordinates of three points, the angles of inclination of the tangents at the extreme points and the linear law of curvature distribution. The second example considers an S-shaped curve with a quadratic law of curvature distributi. References Borysenko, V., Agarkov, O., Pal’ko, K., Pal’ko, M. (2016). Modeling of plane curves in natural parameterization. Geometrychne modeliuvania ta informaciini tekhnologii, 1, 21–27. (in Russian) Borysenko, V. D., Ustenko, S. A., Ustenko, I. V. (2018). Geometric modeling of s-shaped skeletal lines of axial compressor blades profiles. Vestnik dvigatelestroeniia, 1, 45-52. (in Russian). DOI https://doi.org/10.15588/1727-0219-2018-1-7 Burdakov, О. P. (1980). Some globally convergent modifications of Newton's method for solving a system of nonlinear equations. DАN SSSR, 254(3), 521–523. (in Russian) Dennis, J. E., More, J. J. (1977). Quasi-Newton methods, motivation and theorie. SIAM Rew., 19(1), 46–87. Nesterenko, A. N., Khimich, A. N., Yakovlev, M. F. (2006). To the problem of solving of non-linear systems on multi-processor distributed memory computing system. Gerald of computer and information technologies, 10, 54-56. (in Russian) Stetsyuk, P. I., Tkachenko, О. V., Gritsay, O. L. (2020). On constructing the external contour of the Frankl nozzle using quadratic curvature. Cybernetics and Computer Technolog, 1, 23–31. DOI: 10.34229/2707-451X.20.1.3 (in Ukrainian). DOI https://doi.org/10.34229/2707-451x.20.1.3