350 rub
Journal Nonlinear World №5 for 2015 г.
Article in number:
Numerical solution of the problem of a crossing point
Keywords: exterior ballistics crossing point Newton\'s method boundary problem false position method
Authors:
A.T. Bekishev - Dr. Sc. (Eng.), Professor, General Director, General Designer of JSС «Design Bureau «Ametist» (Moscow). E-mail: kb_ametist@mail.ru Yu.B. Korobochkin - Ph. D. (Eng.), Main Research Scientist, JSС «Design Bureau «Ametist» (Moscow). E-mail: korobotchkin@gmail.com
Abstract:
In this paper we consider the problem of finding the point of intersection of the trajectories of two objects, the motion of one of which is described by a system of ordinary differential equations and is controlled by the initial conditions. This problem reduces to a boundary value problem in the theory of ordinary differential equations, which can be reduced to solving a system of nonlinear algebraic equations of a special kind. Discussed in this paper tasks have a distinctive feature. The right part of a system of ordinary differential equations can depend on initial conditions. We produce adaptation of Newton\'s method for solving arisen systems of nonlinear equations, analysis of heuristic false position method, his improvement and a comparison with Newton\'s method. In conclusion, the author analyzes the accuracy of the solution of the crossing point problem for the case of noisy input data.
Pages: 27-37
References

 

  1. Bakhvalov N.S. CHislennye metody. M.: Gl. red. fiz.-mat. lit-ry. 1973.
  2. Kalitkin N.N. CHislennye metody. M.: Nauka. 1978.
  3. Poljak B.T. Metod Njutona i ego rol v optimizacii i vychislitelnojj matematike // Trudy ISA RAN. 2006. T. 26. S. 48−66.
  4. CHujjko V.S. Vneshnjaja ballistika. M.: VVIA im. prof. ZHukovskogo. 1958.
  5. Fikhtengolc G.M. Kurs differencialnogo i integralnogo ischislenija. M.: Fizmatgiz. 1963.