Abstract
In this work a class of singular ordinary differential equations is considered. These problems arise from many engineering and physics applications such as electro-hydrodynamics and some thermal explosions. Adomian decomposition method is applied to solve these singular boundary value problems. The approximate solution is calculated in the form of series with easily computable components. The method is tested for its efficiency by considering four examples and results are compared with previous known results. Techniques that can be applied to obtain higher accuracy of the present method has also been discussed.
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Chawla, M.M., Katti, C.P.: Finite difference methods and their convergence for a class of singular two-point boundary value problems. Numer. Math. 39, 341–350 (1982)
Qu, R., Agarwal, P.: A collocation method for solving a class of singular nonlinear two-point boundary value problems. J. Comput. Appl. Math. 83, 147–163 (1997)
Kumar, M.: A fourth order spline finite difference method for singular two-point boundary value problems. Int. J. Comput. Math. 80, 1499–1504 (2003)
Kumar, M., Aziz, T.: A uniform mesh finite difference method for a class of singular two-point boundary value problems. Appl. Math. Comput. 180, 173–177 (2006)
Pandey, R.K.: On a class of weakly regular singular two point boundary value problems, II. J. Differ. Equ. 127, 110–123 (1996)
Chawla, M.M., Subramanian, R.: A new spline method for singular two-point boundary value problems. J. Inst. Math. Appl. 24, 291 (1988)
Pandey, R.K., Singh, A.K.: On the convergence of a finite difference method for general singular boundary value problems. Int. J. Comput. Math. 80, 1323–1331 (2003)
Wazwaz, A.M.: Adomian decomposition method for a reliable treatment of the EmdenFowler equation. Appl. Math. Comput. 161, 543–560 (2005)
Adomian, G.: Nonlinear Stochastic Systems Theory and Applications to Physics. Kluwer, Dordrecht, Holland (1989)
Adomian, G.: Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Press, Boston (1994)
Adomian, G.: A review of the decomposition method and some recent results for nonlinear equations. Comput. Math. Appl. 21, 101–127 (1989)
Cherruault, Y., Adomian, G.: Decomposition method: a new proof of convergence. Math. Comput. Model. 18(12), 103–106 (1993)
Hosseini, M.M., Nasabzadeh, H.: On the convergence of Adomian decomposition method. Appl. Math. Comput. 44, 13–24 (2006)
Jiao, Y.C., Yamamoto, Y., Dang, C., Hao, Y.: An aftertreatment technique for improving the accuracy of Adomian’s decomposition method. Comput. Math. Appl. 43, 783–798 (2002)
Ghosh, S., Roy, A., Roy, D.: An adaption of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators. Comput. Methods Appl. Mech. Eng. 196, 1133–1153 (2007)
Guellal, S., Grimalt, P., Cherruault, Y.: Numerical study of Lorenz’s equation by the Adomian method. Comput. Math Appl. 33, 25–29 (1997)
Vadasz, P., Olek, S.: Convergence and accuracy of Adomian’s decomposition method for the solution of Lorenz equations. Int. J. Heat Mass Transfer 43, 1715–1734 (2000)
Vadasz, P., Olek, S.: Weak turbulence and chaos for low Prandtl number gravity driven convection in porous media. Transp. Porous Media 37(1), 69–91 (1999)
Vadasz, P.: Local and global transitions to chaos and hysteresis in a porous layer heated from below. Transp. Porous Media 37(2), 213–245 (1999)
Vadasz, P.: Subcritical transitions to chaos and hysteresis in a fluid layer heated from below. Int. J. Heat Mass Transfer 43(5), 705–724 (2000)
Vadasz, P., Olek, S.: Route to chaos for moderate Prandtl number convection in a porous layer heated from below. Transp. Porous Media 41(2), 211–239 (2000)
Repaci, A.: Non-linear dynamical systems: on the accuracy of Adomian’s decomposition method. Appl. Math. Lett. 3, 35–39 (1990)
Mittal, R.C., Nigam, R.: Solution of two dimentional fractional dispersion equations by Adomian decomposition method. In: Proceedings of the 2nd International Congress on Computational Mechanics and Simulation (ICCMS-06), pp. 1636–1640 (2006)
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Mittal, R.C., Nigam, R. Solution of a class of singular boundary value problems. Numer Algor 47, 169–179 (2008). https://doi.org/10.1007/s11075-007-9155-6
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DOI: https://doi.org/10.1007/s11075-007-9155-6