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Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian’s decomposition method. (English) Zbl 1088.65063
Summary: A homotopy perturbation method is proposed to solve quadratic Riccati differential equations. Comparisons are made between Adomian’s decomposition method and the exact solution and the proposed method. The results reveal that the proposed method is very effective and simple.

65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
Full Text: DOI
[1] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Academic Publishers Dordrecht · Zbl 0802.65122
[2] Adomian, G.; Rach, R., On the solution of algebraic equations by the decomposition method, Math. anal. appl., 105, 141-166, (1985) · Zbl 0552.60060
[3] El-Tawil, M.A.; Bahnasawi, A.A.; Abdel-Naby, A., Solving Riccati differential equation using adomian’s decomposition method, Appl. math. comput., 157, 503-514, (2004) · Zbl 1054.65071
[4] Hillermeier, C., Generalized homotopy approach to multiobjective optimization, Int. J. optim. theory appl., 110, 3, 557-583, (2001) · Zbl 1064.90041
[5] He, J.-H., An approximate solution technique depending upon an artificial parameter, Commun. nonlinear sci. simulat., 3, 2, 92-97, (1998) · Zbl 0921.35009
[6] He, J.-H., Variational iteration method: A kind of nonlinear analytical technique: some examples, Int. J. non-linear mech., 34, 4, 699-708, (1999) · Zbl 1342.34005
[7] He, J.-H., Homotopy perturbation technique, Comput. meth. appl. mech. engng., 178, 3/4, 257-262, (1999) · Zbl 0956.70017
[8] He, J.-H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. nonlinear mech., 35, 1, 37-43, (2000) · Zbl 1068.74618
[9] He, J.-H., A review on some new recently developed nonlinear analytical techniques, Int. J. nonlinear sci. numer. simul., 1, 1, 51-70, (2000) · Zbl 0966.65056
[10] He, J.-H., The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. math. comput., 151, 287-292, (2004) · Zbl 1039.65052
[11] He, J.-H., Comparison of homotopy perturbation method and homotopy analysis method, Appl. math. comput., 156, 527-539, (2004) · Zbl 1062.65074
[12] Liao, S.J., An approximate solution technique not depending on small parameters: A special example, Int. J. non-linear mech., 30, 3, 371-380, (1995) · Zbl 0837.76073
[13] Liao, S.J., Boundary element method for general nonlinear differential operators, Eng. anal. boundary element, 20, 2, 91-99, (1997)
[14] Nayfeh, A.H., Problems in perturbation, (1985), John Wiley New York · Zbl 0139.31904
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