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A novel approach for the solution of a class of singular boundary value problems arising in physiology. (English) Zbl 1201.65135
Summary: A new approach implementing a modified decomposition method in combination with the cubic B-spline collocation technique is introduced for the numerical solution of a class of singular boundary value problems arising in physiology. The domain of the problem is split into two subintervals; a modified decomposition procedure based on a special integral operator is implemented in the vicinity of the singular point and outside this domain the resulting boundary value problem is tackled by applying the B-spline scheme. Performance of this method is examined numerically; the examples reveal that the current approach converges to the exact solution rapidly and with O(h 2 ) accuracy. Results show that the method yields a numerical solution in very good agreement with the existing exact and approximate solutions.
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
92C30Physiology (general)
[1]Lin, Hs.: Oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics, J. theor. Biol. 60, 449-457 (1976)
[2]Mcelwain, Dls.: A re-examination of oxygen diffusion in a spherical cell with michaelis-menten oxygen uptake kinetics, J. theor. Biol. 71, 255-263 (1978)
[3]Flesch, U.: The distribution of heat sources in the human head: a theoretical consideration, Journal of theor. Biol. 54, 285-287 (1975)
[4]Garner, J. B.; Shivaji, R.: Diffusion problems with mixed nonlinear boundary condition, Journal of math. Anal. appl. 148, 422-430 (1990) · Zbl 0712.34029 · doi:10.1016/0022-247X(90)90010-D
[5]Kanth, A. S. V. Ravi; Bhattacharya, Vishnu: Cubic spline for a class of non-linear singular boundary value problems arising in physiology, Appl. math. Comput. 174, No. 1, 768-774 (2006) · Zbl 1089.65075 · doi:10.1016/j.amc.2005.05.022
[6]Pandey, R. K.; Singh, Arvind K.: On the convergence of a finite difference method for a class of singular boundary value problems arising in physiology, J. comput. Appl. math. 166, 553-564 (2004) · Zbl 1086.65083 · doi:10.1016/j.cam.2003.09.053
[7]Caglar, Hikmet; Caglar, Nazan; Ozer, Mehmet: B-spline solution of non-linear singular boundary value problems arising in physiology, Chaos solitons fractals 39, 1232-1237 (2009) · Zbl 1197.65107 · doi:10.1016/j.chaos.2007.06.007
[8]Asaithambi, N. S.; Garner, J. B.: Pointwise solution bounds for a class of singular diffusion problems in physiology, Appl. math. Comput. 30, No. 3, 215-222 (1989) · Zbl 0669.92004 · doi:10.1016/0096-3003(89)90053-2
[9]Gustaffsson, B.: A numerical method for solving singular boundary value problems, Numer. math. 21, 328-344 (1973) · Zbl 0255.65032 · doi:10.1007/BF01436387
[10]Kanth, A. S. V. Ravi; Reddy, Y. N.: The method of inner boundary condition for singular boundary value problems, Appl. math. Comput. 139, No. 2–3, 429-436 (2003) · Zbl 1027.65102 · doi:10.1016/S0096-3003(02)00209-6
[11]Kanth, A. S. V. Ravi; Reddy, Y. N.: A numerical method for singular two point boundary value problems via Chebyshev economizition, Appl. math. Comput. 146, No. 2–3, 691-700 (2003) · Zbl 1035.65084 · doi:10.1016/S0096-3003(02)00613-6
[12]Hiltmann, P.; Lory, P.: On oxygen diffusion in a spherical cell with michaelis-menten oxygen uptake kinetics, Bull. math. Biol. 45, 661-664 (1983) · Zbl 0512.92008
[13]Adomian, G.: Solving frontier problems of physics: the decomposition method, (1994)
[14]Deeba, E.; Khuri, S. A.: Nonlinear equations, Wiley encyclopedia of electrical and electronics engineering 14, 562-570 (1999)
[15]Deeba, E. Y.; Khuri, S. A.: A decomposition method for solving the nonlinear Klein-Gordon equation, J. comput. Phys. 124, 442-448 (1996) · Zbl 0849.65073 · doi:10.1006/jcph.1996.0071
[16]Khuri, S. A.: A new approach to bratu’s problem, Appl. math. Comput. 147, 131-136 (2004) · Zbl 1032.65084 · doi:10.1016/S0096-3003(02)00656-2
[17]Khuri, S. A.: A numerical algorithm for solving the troesch’s problem, Int. J. Comput. math. 80, No. 4, 493-498 (2003) · Zbl 1022.65084 · doi:10.1080/0020716022000009228
[18]Khuri, S. A.: On the solution of coupled H-like equations of Chandrasekhar, Appl. math. Comput. 133, No. 2-3, 479-485 (2002) · Zbl 1018.85005 · doi:10.1016/S0096-3003(01)00251-X
[19]Khuri, S. A.: An alternative solution algorithm for the nonlinear generalized Emden-Fowler equation, Int. J. Nonlinear sci. Numeri. simul. 2, 299-302 (2001) · Zbl 1072.34503 · doi:10.1515/IJNSNS.2001.2.3.299
[20]Khuri, S. A.: On the decomposition method for the approximate solution of nonlinear ordinary differential equations, Int. J. Math. ed. Science tech. 32, No. 4, 525-539 (2001) · Zbl 1019.34005 · doi:10.1080/00207390110038286
[21]Khuri, S. A.: A Laplace decomposition algorithm applied to a class of nonlinear differential equations, J. appl. Math. 1, No. 4, 141-155 (2001) · Zbl 0996.65068 · doi:10.1155/S1110757X01000183