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Numerical solution of Troesch’s problem by simple shooting method. (English) Zbl 1191.65100
Summary: This paper describes a simple and efficient approach to the Troesch’s problem. In this approach, the hyperbolic nonlinear term in the equation is first converted into polynomial nonlinear terms by variable transformation, and a simple shooting method is then used directly to solve this transformed problem. The calculated results are in excellent agreement with those obtained by other analytical and numerical methods.

65L10Boundary value problems for ODE (numerical methods)
Full Text: DOI
[1] Weibel, E. S.: On the confinement of a plasma by magnetostatic fields, Phys. fluids 2, No. 1, 52-56 (1959)
[2] Markin, V. S.; Chernenko, A. A.; Chizmadehev, Y. A.; Chirkov, Y. G.: Aspects of the theory of gas porous electrodes, Fuel cells: their electrochemical kinetics, 21-33 (1966)
[3] Gidaspow, D.; Baker, B. S.: A model for discharge of storage batteries, J. electrochem. Soc. 120, 1005-1010 (1973)
[4] B.A. Troesch, Intrinsic difficulties in the numerical solution of a boundary value problem, Internal Report NN -- 142, TRW Inc., Redondo Beach, California, 1960. · Zbl 0117.19604
[5] Roberts, S. M.; Shipman, J. S.: On the closed form solution of troesch’s problem, J. comput. Phys. 21, 291-304 (1976) · Zbl 0334.65062 · doi:10.1016/0021-9991(76)90026-7
[6] Deeba, E.; Khuri, S. A.; Xie, S.: An algorithm for solving boundary value problems, J. comput. Phys. 159, 125-138 (2000) · Zbl 0959.65091 · doi:10.1006/jcph.2000.6452
[7] Khuri, S. A.: A numerical algorithm for solving troesch’s problem, Int. J. Comput. math. 80, 493-498 (2003) · Zbl 1022.65084 · doi:10.1080/0020716022000009228
[8] Momani, S.; Abuasad, S.; Odibat, Z.: Variational iteration method for solving nonlinear boundary value problems, Appl. math. Comput. 183, 1351-1358 (2006) · Zbl 1110.65068 · doi:10.1016/j.amc.2006.05.138
[9] Feng, X.; Mei, L.; He, G.: An efficient algorithm for solving troesch’s problem, Appl. math. Comput. 189, 500-507 (2007) · Zbl 1122.65373 · doi:10.1016/j.amc.2006.11.161
[10] Chang, S. H.; Chang, I. L.: A new algorithm for calculating one-dimensional differential transform of nonlinear functions, Appl. math. Comput. 195, 799-808 (2008) · Zbl 1132.65062 · doi:10.1016/j.amc.2007.05.026
[11] Roberts, S. M.; Shipman, J. S.: Solution of troesch’s two-point boundary value problem by a combination of techniques, J. comput. Phys. 10, 232-241 (1972) · Zbl 0247.65052 · doi:10.1016/0021-9991(72)90063-0
[12] Scott, M. R.: On the conversion of boundary-value problems into stable initial-value problems via several invariant imbedding algorithms, Numerical solutions of boundary-value problems for ordinary differential equations, 89-146 (1975) · Zbl 0335.65032
[13] Snyman, J. A.: Continuous and discontinuous numerical solutions to the troesch problem, J. comput. Appl. math. 5, 171-175 (1979) · Zbl 0419.65047 · doi:10.1016/0377-0427(79)90002-5
[14] Jones, D. J.: Solutions of troesch’s and other two-point boundary-value problems by shooting techniques, J. comput. Phys. 12, 429-434 (1973) · Zbl 0264.65046 · doi:10.1016/0021-9991(73)90165-4
[15] Kubicek, M.; Hlavacek, V.: Solution of troesch’s two-point boundary value problem by shooting technique, J. comput. Phys. 17, 95-101 (1975) · Zbl 0301.65047 · doi:10.1016/0021-9991(75)90066-2
[16] Troesch, B. A.: A simple approach to a sensitive two-point boundary value problem, J. comput. Phys. 21, 279-290 (1976) · Zbl 0334.65063 · doi:10.1016/0021-9991(76)90025-5
[17] Strauss, M.; Ring, T. A.; Bowen, H. K.: Osmotic pressure for concentrated suspensions of polydisperse particles with thick double layers, J. colloid interface sci. 118, No. 2, 326-334 (1987)
[18] Acton, F. S.: Numerical methods that work, (1990) · Zbl 0746.65001