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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.
MSC:
65L10Boundary value problems for ODE (numerical methods)
References:
[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.
[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