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

Document Type : Article


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

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

3 Higher Technological Institute, Tenth of Ramadan City, Egypt


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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