A new extended B-spline approximation technique for second order singular boundary value problems arising in physiology

Volume 19, Issue 4, pp 258--267 http://dx.doi.org/10.22436/jmcs.019.04.06

Publication Date: July 10, 2019 Submission Date: April 23, 2019 Revision Date: June 12, 2019 Accteptance Date: June 15, 2019

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Authors

Imtiaz Wasim - Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan. Muhammad Abbas - Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan. Muhammad Kashif Iqbal - Department of Mathematics, , Government College University, Faisalabad, 38000, Pakistan.

Abstract

In this study, we have explored the approximate solution of \(2^{nd}\) order singular boundary value problems (SBVP's) using extended cubic B-spline (ECBS) collocation approach. The accuracy of the numerical algorithm has been enhanced by means of a novel ECBS approximation for $2^{nd}$ order derivative. To endorse our claim, few test examples have been considered and the experimental results are compared with the already existing methods. It is observed that the proposed technique is more accurate and efficient in comparison to the existing techniques on the topic.

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Keywords

• Singular boundary value problems
• extended B-spline functions
• quasi-linearization technique
• extended B-spline collocation method

MSC

•  34B15
•  34B16
•  74H15
•  65L10
•  65L11

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