Applications of the differential transformation to three-point singular boundary value problems for ordinary differential equations

Volume 29, Issue 1, pp 73--89 http://dx.doi.org/10.22436/jmcs.029.01.07

Publication Date: August 11, 2022 Submission Date: June 03, 2022 Revision Date: June 15, 2022 Accteptance Date: June 23, 2022

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Authors

G. Methi - Department of Mathematics \(\&\) Statistics, Manipal University Jaipur, Rajasthan, India. A. Kumar - Department of Mathematics \(\&\) Statistics, Manipal University Jaipur, Rajasthan, India. J. Rebenda - Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 8, 616 00 Brno, Czech Republic.

Abstract

The differential transform method is used to find numerical approximations of the solution to a class of certain nonlinear three-point singular boundary value problems. The method is based on Taylor's theorem. Coefficients of the Taylor series are determined by constructing a recurrence relation. To deal with the nonlinearity of the problems, the Faa di Bruno's formula containing the partial ordinary Bell polynomials is applied within the differential transform. The error estimation results are also presented. Four concrete problems are studied to show efficiency and reliability of the method. The obtained results are compared to other methods, e.g., reproducing kernel Hilbert space method.

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Keywords

• Differential transform method
• singular boundary value problems
• numerical approximation
• partial ordinary Bell polynomials
• error estimates

MSC

•  34B16
•  65L10

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