A septic B-spline collocation method for solving nonlinear singular boundary value problems arising in physiological models

Document Type : Article

Authors

1 Department of Mathematics, Faculty of Science, University of Menoufia, Shebein El-Koom, Egypt.

2 Department of Mathematics, Faculty of Science, University of Al-Azhar, Cairo, Nasr-City, Egypt.

3 Department of Basic Science, Higher Technological Institute, 10th of Ramadan City, Egypt

Abstract

In this paper, we present a numerical method based on septic B-spline function for nonlinear singular second-order two-point boundary value problems, which depend on different physiological processes as thermal explosions problem and the steady state oxygen diffusion in a spherical cell with Michaelis–Menten uptake kinetics and distribution of heat sources in the human head. Septic B-spline method has a truncation error of O(h^8) and converges to the exact solution with O(h^6). The numerical problems show that our method is very effective. The resulting sets of differential equations are modified at the singular point and are treated by using septic B-spline for finding the numerical solution. The maximum absolute errors and the absolute residual errors are acceptable.

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References

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Scientia Iranica
Volume 27, Issue 3
Transactions on Industrial Engineering (E)
May and June 2020
Pages 1674-1874

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History

  • Receive Date: 30 May 2018
  • Revise Date: 01 October 2018
  • Accept Date: 29 December 2018

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