A Family of Functionally-Fitted Third Derivative Block Falkner Methods for Solving Second-Order Initial-Value Problems with Oscillating Solutions

Higinio Ramos, Ridwanulahi Abdulganiy, Ruth Olowe and Samuel Jator
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Higinio Ramos: Department of Applied Mathematics, Universidad de Salamanca, 37008 Salamanca, Spain
Ridwanulahi Abdulganiy: Distance Learning Institute, University of Lagos, Lagos Mainland 101017, Nigeria
Ruth Olowe: Department of Mathematics, University of Lagos, Lagos Mainland 101017, Nigeria
Samuel Jator: Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USA

Mathematics, 2021, vol. 9, issue 7, 1-22

Abstract: 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.

Keywords: adapted Falkner methods; algebraic order; block methods; oscillatory solutions; second order initial-value-problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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