The Application of Quartic Trigonometric B-spline for Solving Second Order Singular Boundary Value Problems

Authors

  • Tayyaba Akram School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang
  • Muhammad Abbas Department of Mathematics, University of Sargodha, 40100 Sargodha
  • Ahmad Izani Ismail School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang

DOI:

https://doi.org/10.26713/cma.v9i3.832

Keywords:

Quartic trigonometric basis functions, Trigonometric collocation method, Singular boundary value problem

Abstract

In this paper, a quartic trigonometric B-spline collocation approach is described and presented for the numerical solution of the second order singular boundary value problems. Several numerical examples are discussed to exhibit the feasibility and capability of the technique. The unknown coefficients \(C_{i}\), \(i=-4,-3,\ldots,n-1\) are obtained through optimization. The maximum errors \((L_{\infty})\) and norm errors \((L_{2})\) are also computed for different space size steps to assess the performance of the proposed technique. The rate of convergence is discussed numerically to be of fourth-order. The numerical solutions are contrasted with both analytical and other existing numerical solutions that exist in the literature. The comparison shows that the quartic trigonometric B-spline method is superior as it yields more accurate solutions.

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Published

25-09-2018
CITATION

How to Cite

Akram, T., Abbas, M., & Ismail, A. I. (2018). The Application of Quartic Trigonometric B-spline for Solving Second Order Singular Boundary Value Problems. Communications in Mathematics and Applications, 9(3), 433–445. https://doi.org/10.26713/cma.v9i3.832

Issue

Vol. 9 No. 3 (2018)

Section

Research Article

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