Jang, T. S. Pseudo-parameter iteration method (PIM): a semi-analytic solution procedure for nonlinear problems. (English) Zbl 07323676 Commun. Nonlinear Sci. Numer. Simul. 97, Article ID 105733, 20 p. (2021). MSC: 65L99 65L05 × Cite Format Result Cite Review PDF Full Text: DOI
Radid, Atika; Rhofir, Karim SOR-like new iterative method for solving the epidemic model and the prey and predator problem. (English) Zbl 1459.92143 Discrete Dyn. Nat. Soc. 2020, Article ID 9053754, 13 p. (2020). MSC: 92D30 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Sardanyés, Josep; Rodrigues, Carla; Januário, Cristina; Martins, Nuno; Gil-Gómez, Gabriel; Duarte, Jorge Activation of effector immune cells promotes tumor stochastic extinction: a homotopy analysis approach. (English) Zbl 1338.92052 Appl. Math. Comput. 252, 484-495 (2015). MSC: 92C50 92-08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Shamsyeh Zahedi, Moosarreza; Saberi Nik, Hassan On homotopy analysis method applied to linear optimal control problems. (English) Zbl 1427.49035 Appl. Math. Modelling 37, No. 23, 9617-9629 (2013). MSC: 49M20 65L99 49N05 × Cite Format Result Cite Review PDF Full Text: DOI
Fardi, Mojtaba; Kazemi, Ebrahim; Ezzati, Reza; Ghasemi, Mehdi Periodic solution for strongly nonlinear vibration systems by using the homotopy analysis method. (English) Zbl 1278.74186 Math. Sci., Springer 6, Paper No. 65, 5 p. (2012). MSC: 74S30 74H45 65M99 × Cite Format Result Cite Review PDF Full Text: DOI
Asaithambi, Asai Numerical solution of a third-order nonlinear boundary-value problem by automatic differentiation. (English) Zbl 1218.65073 Int. J. Comput. Math. 88, No. 7, 1484-1496 (2011). MSC: 65L10 34B15 × Cite Format Result Cite Review PDF Full Text: DOI
Liao, Shijun An optimal homotopy-analysis approach for strongly nonlinear differential equations. (English) Zbl 1222.65088 Commun. Nonlinear Sci. Numer. Simul. 15, No. 8, 2003-2016 (2010). MSC: 65L99 34A25 34A45 × Cite Format Result Cite Review PDF Full Text: DOI
Kargarnovin, Mohammad H.; Jafari-Talookolaei, Ramazan A. Application of the homotopy method for the analytic approach of the nonlinear free vibration analysis of the simple end beams using four engineering theories. (English) Zbl 1397.74089 Acta Mech. 212, No. 3-4, 199-213 (2010). MSC: 74H45 74K10 74H10 74H05 × Cite Format Result Cite Review PDF Full Text: DOI
Biazar, Jafar; Ayati, Zainab; Yaghouti, Mohammad Reza Homotopy perturbation method for homogeneous Smoluchowsk’s equation. (English) Zbl 1197.65220 Numer. Methods Partial Differ. Equations 26, No. 5, 1146-1153 (2010). MSC: 65R20 45K05 45G05 × Cite Format Result Cite Review PDF Full Text: DOI
Liao, Shijun Notes on the homotopy analysis method: some definitions and theorems. (English) Zbl 1221.65126 Commun. Nonlinear Sci. Numer. Simul. 14, No. 4, 983-997 (2009). MSC: 65H99 35A25 35C10 × Cite Format Result Cite Review PDF Full Text: DOI
Singh, Om P.; Pandey, Rajesh K.; Singh, Vineet K. An analytic algorithm of Lane-Emden type equations arising in astrophysics using modified homotopy analysis method. (English) Zbl 1198.65250 Comput. Phys. Commun. 180, No. 7, 1116-1124 (2009). MSC: 65N99 35Q85 85A05 × Cite Format Result Cite Review PDF Full Text: DOI
Goh, S. M.; Noorani, M. S. M.; Hashim, I. Efficacy of variational iteration method for chaotic genesio system - classical and multistage approach. (English) Zbl 1198.65140 Chaos Solitons Fractals 40, No. 5, 2152-2159 (2009). MSC: 65L99 × Cite Format Result Cite Review PDF Full Text: DOI
Bokhari, Ashfaque H.; Mohammad, Ghulam; Mustafa, M. T.; Zaman, F. D. Adomian decomposition method for a nonlinear heat equation with temperature dependent thermal properties. (English) Zbl 1181.80002 Math. Probl. Eng. 2009, Article ID 926086, 12 p. (2009). MSC: 80A20 80M25 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Rahman, M. A.; Mustafiz, S.; Biazar, J.; Koksal, M.; Islam, M. R. Investigation of a novel perforation technique in petroleum wells-perforation by drilling. (English) Zbl 1269.76119 J. Franklin Inst. 344, No. 5, 777-789 (2007). MSC: 76S05 × Cite Format Result Cite Review PDF Full Text: DOI Link
Ghosh, S.; Roy, A.; Roy, D. An adaptation of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators. (English) Zbl 1120.70303 Comput. Methods Appl. Mech. Eng. 196, No. 4-6, 1133-1153 (2007). MSC: 70-08 70K55 × Cite Format Result Cite Review PDF Full Text: DOI
Makinde, O. D. Adomian decomposition approach to a SIR epidemic model with constant vaccination strategy. (English) Zbl 1109.92041 Appl. Math. Comput. 184, No. 2, 842-848 (2007). MSC: 92D30 65L99 × Cite Format Result Cite Review PDF Full Text: DOI
Makinde, O. D. Solving ratio-dependent predator-prey system with constant effort harvesting using Adomian decomposition method. (English) Zbl 1114.65081 Appl. Math. Comput. 186, No. 1, 17-22 (2007). MSC: 65L05 34A34 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Chun, Changbum Construction of Newton-like iteration methods for solving nonlinear equations. (English) Zbl 1126.65042 Numer. Math. 104, No. 3, 297-315 (2006). MSC: 65H05 65H20 × Cite Format Result Cite Review PDF Full Text: DOI
Biazar, J.; Tango, M.; Islam, R. Ozone decomposition of the second order in aqueous solutions. (English) Zbl 1102.76076 Appl. Math. Comput. 177, No. 1, 220-225 (2006). MSC: 76V05 76M25 80A20 × Cite Format Result Cite Review PDF Full Text: DOI
Biazar, J.; Tango, M.; Islam, R. Ozone decomposition of the second order in aqueous solutions. (English) Zbl 1331.65114 Appl. Math. Comput. 177, No. 1, 220-225 (2006). MSC: 65L99 34C60 92E20 × Cite Format Result Cite Review PDF Full Text: DOI
Biazar, J.; Ilie, M.; Khoshkenar, A. An improvement to an alternate algorithm for computing Adomian polynomials in special cases. (English) Zbl 1091.65053 Appl. Math. Comput. 173, No. 1, 582-592 (2006). MSC: 65J15 47J25 65R20 45G10 65L05 34A34 35L60 65M70 35K55 45J05 × Cite Format Result Cite Review PDF Full Text: DOI
Biazar, J.; Amirtaimoori, A. R. An analytic approximation to the solution of heat equation by Adomian decomposition method and restrictions of the method. (English) Zbl 1090.65118 Appl. Math. Comput. 171, No. 2, 738-745 (2005). MSC: 65M70 35K15 × Cite Format Result Cite Review PDF Full Text: DOI
Biazar, J.; Montazeri, R. A computational method for solution of the prey and predator problem. (English) Zbl 1060.65612 Appl. Math. Comput. 163, No. 2, 841-847 (2005). MSC: 65L05 34A34 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Biazar, J.; Islam, R. Solution of wave equation by Adomian decomposition method and the restrictions of the method. (English) Zbl 1038.65100 Appl. Math. Comput. 149, No. 3, 807-814 (2004). MSC: 65M70 35L05 × Cite Format Result Cite Review PDF Full Text: DOI
Abdelwahid, Fawzi A mathematical model of Adomian polynomials. (English) Zbl 1027.65072 Appl. Math. Comput. 141, No. 2-3, 447-453 (2003). MSC: 65J15 47J25 65Y15 × Cite Format Result Cite Review PDF Full Text: DOI
Biazar, J.; Babolian, E.; Kember, G.; Nouri, A.; Islam, R. An alternate algorithm for computing Adomian polynomials in special cases. (English) Zbl 1027.65076 Appl. Math. Comput. 138, No. 2-3, 523-529 (2003). MSC: 65J15 35K05 45G15 65R20 47J25 35L60 65M70 × Cite Format Result Cite Review PDF Full Text: DOI
Liao, Shijun A new analytic algorithm of Lane–Emden type equations. (English) Zbl 1022.65078 Appl. Math. Comput. 142, No. 1, 1-16 (2003). MSC: 65L05 34A34 65L20 85-08 85A15 × Cite Format Result Cite Review PDF Full Text: DOI
Babolian, E.; Biazar, J. On the order of convergence of Adomian method. (English) Zbl 1044.65043 Appl. Math. Comput. 130, No. 2-3, 383-387 (2002). Reviewer: M. Thamban Nair (Chennai) MSC: 65J15 47J25 × Cite Format Result Cite Review PDF Full Text: DOI
Laffez, P.; Abbaoui, K. Modelling of the thermic exchanges during a drilling. Resolution with Adomian’s decomposition method. (English) Zbl 0854.76094 Math. Comput. Modelling 23, No. 10, 11-14 (1996). MSC: 76T99 80A20 86A20 00A71 × Cite Format Result Cite Review PDF Full Text: DOI
Abbaoui, K.; Cherruault, Y. Convergence of Adomian’s method applied to differential equations. (English) Zbl 0809.65073 Comput. Math. Appl. 28, No. 5, 103-109 (1994). Reviewer: K.T.S.Iyengar (Bangalore) MSC: 65L05 34A34 × Cite Format Result Cite Review PDF Full Text: DOI
Adomian, G. A review of the decomposition method and some recent results for nonlinear equations. (English) Zbl 0732.35003 Comput. Math. Appl. 21, No. 5, 101-127 (1991). Reviewer: G.Aniculaesei (Iaşi) MSC: 35A25 35R60 35G20 × Cite Format Result Cite Review PDF Full Text: DOI
Cherruault, Y. Convergence of Adomian’s method. (English) Zbl 0728.65056 Math. Comput. Modelling 14, 83-86 (1990). Reviewer: J.Vaníček (Praha) MSC: 65J15 47J25 × Cite Format Result Cite Review PDF Full Text: DOI
Adomian, G. A review of the decomposition method and some recent results for nonlinear equations. (English) Zbl 0713.65051 Math. Comput. Modelling 13, No. 7, 17-43 (1990). Reviewer: G.Stoyan MSC: 65L10 65J99 34B15 × Cite Format Result Cite Review PDF Full Text: DOI
Cherruault, Yves Convergence of Adomian’s method. (English) Zbl 0697.65051 Kybernetes 18, No. 2, 31-38 (1989). Reviewer: A.Donescu MSC: 65J15 47J25 × Cite Format Result Cite Review PDF Full Text: DOI
Adomian, G. A review of the decomposition method in applied mathematics. (English) Zbl 0671.34053 J. Math. Anal. Appl. 135, No. 2, 501-544 (1988). Reviewer: L.Pastur MSC: 34F05 60H10 34A34 35R60 × Cite Format Result Cite Review PDF Full Text: DOI