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Ramos Calle, Higinio Abdulganiy, Ridwanulahi Olowe, Ruth Jator, Samuel 2024-03-14T11:24:13Z 2024-03-14T11:24:13Z 2021 Ramos, H.; Abdulganiy, R.; Olowe, R.; Jator, S. A Family of Functionally-Fitted Third Derivative Block Falkner Methods for Solving Second-Order Initial-Value Problems with Oscillating Solutions. Mathematics 2021, 9, 713. https://doi.org/10.3390/math9070713 http://hdl.handle.net/10366/156662 10.3390/math9070713 2227-7390 [EN]One of the well-known schemes for the direct numerical integration of second-order initial-value problems is due to Falkner. This paper focuses on the construction of a family of adapted block Falkner methods which are frequency dependent for the direct numerical solution of second-order initial value problems with oscillatory solutions. The techniques of collocation and interpolation are adopted here to derive the new methods. The study of the properties of the proposed adapted block Falkner methods reveals that they are consistent and zero-stable, and thus, convergent. Furthermore, the stability analysis and the algebraic order conditions of the proposed methods are established. As may be seen from the numerical results, the resulting family is efficient and competitive compared to some recent methods in the literature. eng MDPI Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Adapted Falkner methods Algebraic order Block methods Oscillatory solutions Second order initial-value-problems 12 Matemáticas A Family of Functionally-Fitted Third Derivative Block Falkner Methods for Solving Second-Order Initial-Value Problems with Oscillating Solutions. info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://doi.org/10.3390/math9070713 Mathematics 9 7 713