B-spline solution of non-linear singular boundary value problems arising in physiology

Chaos, Solitons & Fractals - Tập 39 - Trang 1232-1237 - 2009
Hikmet Çağlar1, Nazan Çağlar2, Mehmet Özer3
1Istanbul Kultur University, Department of Mathematics-Computer, Atakoy Campus, Bakirkoy, 34156 Istanbul, Turkey
2Istanbul Kultur University, Department of Business Administration, Atakoy Campus, Bakirkoy, 34156 Istanbul, Turkey
3Istanbul Kultur University, Department of Physics, Atakoy Campus, Bakirkoy, 34156 Istanbul, Turkey

Tài liệu tham khảo

Caglar, 1999, The numerical solution of third-order boundary-value problems with fourth-degree B-spline functions, Int J Comput Math, 71, 373, 10.1080/00207169908804816 Caglar, 1999, The numerical solution of fifth-order boundary-value problems with sixth-degree B-spline functions, Appl Math Lett, 12, 25, 10.1016/S0893-9659(99)00052-X Caglar, 2003, Spline solution of nonlinear beam problems, J Concr Appl Math, 1, 253 Caglar, 2006, B-spline interpolation compared with finite difference, finite element and finite volume methods which applied to two-point boundary value problems, Appl Math Comput, 175, 72, 10.1016/j.amc.2005.07.019 Caglar, 2006, B-spline solution of singular boundary value problems, Appl Math Comput, 10.1016/j.amc.2006.05.035 Chawla, 1984, A finite difference method for a class of singular two point boundary value problems, IMA J Numer Anal, 4, 457, 10.1093/imanum/4.4.457 Kanth, 2003, A numerical method for singular boundary value problems via Chebyshev economization, Appl Math Comput, 146, 691, 10.1016/S0096-3003(02)00613-6 Kanth, 2005, Cubic spline for a class of singular two-point boundary value problems, Appl Math Comput, 170, 733, 10.1016/j.amc.2004.12.049 Kanth, 2006, Cubic spline for a class of non-linear singular boundary value problems arising in physiology, Appl Math Comput, 174, 768, 10.1016/j.amc.2005.05.022 Kanth, 2007, Cubic spline polynomial for non-linear two-point boundary value problems, Appl Math Comput Caglar N, Caglar H. B-spline solution of singular boundary value problems. Appl Math Comput. doi:10.1016/j.amc.2006.05.035. Hiltmann, 1983, On oxygen diffusion in a spherical cell with Michaelis–Menten oxygen uptake kinetics, Bull Math Biol, 45, 661, 10.1007/BF02460043 Anderson, 1983, Analytical diffusion in a spherical cell with Michaelis–Menten oxygen uptake kinetics, Bull Math Biol, 47, 145, 10.1016/S0092-8240(85)90009-6 Adam, 1986, A simplified mathematical model of tumor growth, Math Biosci, 81, 224, 10.1016/0025-5564(86)90119-7 Asaithambi, 1989, Point wise bounds for a class of singular diffusion problem in physiology, Appl Math Comput, 30, 215, 10.1016/0096-3003(89)90053-2 Lin, 1976, Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, J Theor Biol, 60, 449, 10.1016/0022-5193(76)90071-0 McElwain, 1978, A re-examination of oxygen diffusion in a spherical cell with Michaelis–Menten oxygen uptake kinetics, J Theor Biol, 71, 255, 10.1016/0022-5193(78)90270-9 Flesch, 1975, The distribution of heat sources in the human head: a theoretical consideration, J Theor Biol, 54, 285, 10.1016/S0022-5193(75)80131-7 Garner, 1990, Diffusion problems with mixed nonlinear boundary condition, J Math Anal Appl, 148, 422, 10.1016/0022-247X(90)90010-D Duggan, 1986, Point wise bounds for a nonlinear heat conduction model of the human head, Bull Math Biol, 48, 229, 10.1007/BF02460025 de Boor, 1978 Golub, 1992 Fletcher, 1987