International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

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 Volume 7, Issue 6 (June 2020), Pages: 48-56

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 Original Research Paper

 Title: Numerical treatment of fourth-order singular boundary value problems using new quintic B-spline approximation technique

 Author(s): Muhammad Kashif Iqbal 1, Muhammad Waseem Iftikhar 2, Muhammad Shahid Iqbal 3, Muhammad Abbas 4, *

 Affiliation(s):

 1Department of Mathematics, Government College University, Faisalabad, Pakistan
 2Department of Mathematics, National Textile University, Faisalabad, Pakistan
 3Department of Mathematics, University of Okara, Okara, Pakistan
 4Department of Mathematics, University of Sargodha, Sargodha, Pakistan

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-0491-1528

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2020.06.007

 Abstract:

Singular boundary value problems (SBVPs) are cropped up in mathematical modeling of many real-life phenomena such as chemical reactions, electro-hydrodynamics, aerodynamics, thermal explosions, fluid dynamics, and atomic nuclear reactions. In this work, a new quintic B-spline approximation technique has been presented for the numerical solution of fourth-order singular boundary value problems. The fifth-degree basis spline functions are brought into play together with a new approximation for fourth-order derivative. The proposed numerical technique is proved to be uniformly convergent in the entire domain. In order to corroborate this work, the proposed scheme has been implemented on some test problems. The comparison of computational outcomes advocates the superior performance of the presented algorithm over current methods on the topic. 

 © 2020 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Singular boundary value problems, Quintic B-spline functions, Quintic B-spline collocation method, Emden flower type equations

 Article History: Received 4 October 2019, Received in revised form 8 March 2020, Accepted 11 March 2020

 Acknowledgment:

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The authors declare that they have no conflict of interest.

 Citation:

 Iqbal MK, Iftikhar MW, and Iqbal MS et al. (2020). Numerical treatment of fourth-order singular boundary value problems using new quintic B-spline approximation technique. International Journal of Advanced and Applied Sciences, 7(6): 48-56

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 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5

 Tables

 Table 1 Table 2 Table 3 Table 4 Table 5

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