 An efficient variable step-size rational Falkner-type method for solving the special second-order IVPHiginio Ramos, Gurjinder Singh, V. Kanwar and Saurabh Bhatia Applied Mathematics and Computation, 2016, vol. 291, issue C, 39-51 Abstract: In this paper, firstly a rational one-parameter family of Falkner-type explicit methods is presented for directly solving numerically special second order initial value problems in ordinary differential equations. The proposed family of methods has second algebraic order of convergence. Imposing that the principal term of the local truncation error of the proposed family vanishes, we get an expression for the free parameter at the grid point (xn, yn). By substituting this value of the free parameter in the family, a new rational third order method is obtained. Further, by combining the third order method with any member of the second order family, their variable step-size formulation as an embedded pair is considered. Some numerical experiments are given to illustrate the performance and efficiency of the proposed methods. Keywords: Ordinary differential equations; Initial value problems; Rational method; Special second order differential equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:291:y:2016:i:c:p:39-51 DOI: 10.1016/j.amc.2016.06.033 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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