TY - JOUR TI - Cubically convergent method for solving a standard boundary value problem AU - Palej, Rafał TI - Cubically convergent method for solving a standard boundary value problem AB - 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. VL - 2013 IS - Mechanika Zeszyt 1-M (5) 2013 PY - 2014 SN - 0011-4561 C1 - 2353-737X SP - 293 EP - 299 DO - 10.4467/2353737XCT.14.037.1963 UR - https://ejournals.eu/czasopismo/czasopismo-techniczne/artykul/cubically-convergent-method-for-solving-a-standard-boundary-value-problem KW - shooting method KW - sensitivity functions KW - derivatives of sensitivity functions KW - cubic convergence