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Siddiqi, Shahid S.; Iftikhar, Muzammal

Numerical solution of higher order boundary value problems. (English) Zbl 1416.65216

Abstr. Appl. Anal. 2013, Article ID 427521, 12 p. (2013).
Summary: The aim of this paper is to use the homotopy analysis method (HAM), an approximating technique for solving linear and nonlinear higher order boundary value problems. Using HAM, approximate solutions of seventh-, eighth-, and tenth-order boundary value problems are developed. This approach provides the solution in terms of a convergent series. Approximate results are given for several examples to illustrate the implementation and accuracy of the method. The results obtained from this method are compared with the exact solutions and other methods [G. Akram and H. U. Rehman, Numer. Algorithms 62, No. 3, 527–540 (2013; Zbl 1281.65101); K. Farajeyan and N. R. Maleki, “Numerical solution of tenth-order boundary value problems in off step points,” J. Basic Appl. Sci. Res. 2, No. 6, 6235–6244 (2012); F. Geng and X. Li, Math. Sci. Q. J. 3, No. 2, 161–172 (2009; Zbl 1206.65203); A. Golbabai and M. Javidi, Appl. Math. Comput. 191, No. 2, 334–346 (2007; Zbl 1193.65148); J.-H. He, Phys. Scr. 76, No. 6, 680–682 (2007; Zbl 1134.34307); M. Inc and D. J. Evans, Int. J. Comput. Math. 81, No. 6, 685–692 (2004; Zbl 1060.65078); A. Lamnii et al., Appl. Math. E-Notes 8, 171–178 (2008; Zbl 1159.65077); the first author and G. Akram, Int. J. Comput. Math. 84, No. 3, 347–368 (2007; Zbl 1117.65115); the first author et al., “Solution of seventh order boundary value problem by differential transformation method”, World Appl. Sci. J. 16, No. 11, 1521–1526 (2012); the first author et al., “Solution of tenth order boundary value problems using variational iteration technique,” Eur. J. Sci. Res. 30, No. 3, 326–347 (2009); the authors, “Solution of seventh order boundary value problems by variation of parameters method,” Res. J. Appl. Sci., Eng. Technol. 5, No. 1, 176–179 (2013); the first author and E. H. Twizell, Comput. Methods Appl. Mech. Eng. 131, No. 3–4, 309–325 (1996; Zbl 0881.65076); the first author and E. H. Twizell, Int. J. Comput. Math. 68, No. 3–4, 345–362 (1998; Zbl 0920.65049); M. Torvattanabun and S. Koonprasert, Thai J. Math. 8, 121–129 (2010; Zbl 1238.65087); K. N. S. KasiViswanadham and Y. S. Raju, “Quintic B-spline collocation method for tenth order boundary value problems”, Int. J. Comput. Appl. 51, No. 15, 7–13 (2012; doi:10.5120/8116-1735)] revealing that the present method is more accurate.

Cited in 7 Documents

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations

Citations:

Zbl 1281.65101; Zbl 1206.65203; Zbl 1193.65148; Zbl 1134.34307; Zbl 1060.65078; Zbl 1159.65077; Zbl 1117.65115; Zbl 0881.65076; Zbl 0920.65049; Zbl 1238.65087
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