%0 Journal Article
%T A septic B-spline collocation method for solving nonlinear singular boundary value problems arising in physiological models
%J Scientia Iranica
%I Sharif University of Technology
%Z 1026-3098
%A Hadhoud, A.R.
%A Ali, K.K.
%A shaalan, M.A.
%D 2020
%\ 06/01/2020
%V 27
%N 3
%P 1674-1874
%! A septic B-spline collocation method for solving nonlinear singular boundary value problems arising in physiological models
%K Septic B-spline collocation method
%K Singular boundary value problems
%K Absolute residual errors
%K Error estimation
%K Uniform convergence
%R 10.24200/sci.2018.51012.1961
%X 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 Michaelisâ€“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.
%U http://scientiairanica.sharif.edu/article_21202_4aa4eac8a4a53d346aee73df2332f1bd.pdf