@article{9a55473d-c0cb-42e6-b9c8-91fd6bd18015,
author = {Rafał Palej},
title = {Cubically convergent method for solving a standard boundary value problem},
journal = {Czasopismo Techniczne},
volume = {2013},
number = {Mechanika Zeszyt 1-M (5) 2013},
year = {2014},
issn = {0011-4561},
pages = {293-299},keywords = {shooting method; sensitivity functions; derivatives of sensitivity functions; cubic convergence},
abstract = {The paper presents a cubically convergent method for solving a standard boundary value problem consisting of n coupled first-order differential equations and n boundary conditions. The idea of the presented method is based on the shooting method using the expansion of the desired function into Taylor’s series including second-order derivatives. Effective use of the iteration formula requires introduction of sensitivity functions and their derivatives. In each iteration, the initial problem, composed of n(1+ n1+ n21 ) first-order differential equations, must be solved, where n1 signifies the number of unknown parameters. The convergence of the presented method has been illustrated on an example.},
doi = {10.4467/2353737XCT.14.037.1963},
url = {https://ejournals.eu/czasopismo/czasopismo-techniczne/artykul/cubically-convergent-method-for-solving-a-standard-boundary-value-problem}
}