Applications of the differential transformation to threepoint singular boundary value problems for ordinary differential equations
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 threepoint 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.
Share and Cite
ISRP Style
G. Methi, A. Kumar, J. Rebenda, Applications of the differential transformation to threepoint singular boundary value problems for ordinary differential equations, Journal of Mathematics and Computer Science, 29 (2023), no. 1, 7389
AMA Style
Methi G., Kumar A., Rebenda J., Applications of the differential transformation to threepoint singular boundary value problems for ordinary differential equations. J Math Comput SCIJM. (2023); 29(1):7389
Chicago/Turabian Style
Methi, G., Kumar, A., Rebenda, J.. "Applications of the differential transformation to threepoint singular boundary value problems for ordinary differential equations." Journal of Mathematics and Computer Science, 29, no. 1 (2023): 7389
Keywords
 Differential transform method
 singular boundary value problems
 numerical approximation
 partial ordinary Bell polynomials
 error estimates
MSC
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