TY - JOUR
ID - 21202
TI - A septic B-spline collocation method for solving nonlinear singular boundary value problems arising in physiological models
JO - Scientia Iranica
JA - SCI
LA - en
SN - 1026-3098
AU - Hadhoud, A.R.
AU - Ali, K.K.
AU - shaalan, M.A.
AD - Department of Mathematics, Faculty of Science, University of Menoufia, Shebein El-Koom, Egypt.
AD - Department of Mathematics, Faculty of Science, University of Al-Azhar, Cairo, Nasr-City, Egypt.
AD - Department of Basic Science, Higher Technological Institute, 10th of Ramadan City, Egypt
Y1 - 2020
PY - 2020
VL - 27
IS - 3
SP - 1674
EP - 1874
KW - Septic B-spline collocation method
KW - Singular boundary value problems
KW - Absolute residual errors
KW - Error estimation
KW - Uniform convergence
DO - 10.24200/sci.2018.51012.1961
N2 - 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.
UR - http://scientiairanica.sharif.edu/article_21202.html
L1 - http://scientiairanica.sharif.edu/article_21202_4aa4eac8a4a53d346aee73df2332f1bd.pdf
ER -