Aminikhah, Hossein The combined Laplace transform and new homotopy perturbation methods for stiff systems of ODEs. (English) Zbl 1252.34018 Appl. Math. Modelling 36, No. 8, 3638-3644 (2012). Summary: We propose new technique for solving stiff system of ordinary differential equations. This algorithm is based on Laplace transform and homotopy perturbation methods. The new technique is applied to solving two mathematical models of stiff problem. We show that the present approach is relatively easy, efficient and highly accurate. Cited in 15 Documents MSC: 34A45 Theoretical approximation of solutions to ordinary differential equations 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. Keywords:Laplace transform method; new homotopy perturbation method; stiff system of ordinary differential equations PDFBibTeX XMLCite \textit{H. Aminikhah}, Appl. Math. Modelling 36, No. 8, 3638--3644 (2012; Zbl 1252.34018) Full Text: DOI References: [1] Flaherty, J. E.; OMalley, R. E., The numerical solution of boundary value problems for stiff differential equations, Math. Comput., 31, 66-93 (1997) [2] Bui, T. D.; Bui, T. R., Numerical methods for extremely stiff systems of ordinary differential equations, Appl. Math. Modell., 3, 355-358 (1979) · Zbl 0438.65074 [3] Butcher, J. C., Numerical Methods for Ordinary Differential Equations (2003), Wiley: Wiley New York · Zbl 1032.65512 [4] Ixaru, L. Gr.; Vanden Berghe, G.; De Meyer, H., Frequency evaluation in exponential fitting multistep algorithms for ODEs, J. Comput. Appl. Math., 140, 423-434 (2000) · Zbl 0996.65075 [5] P. Kaps, Rosenbrock-type methods, in: G. Dahlquist, R. Jeltsch, (Eds.), Numerical methods for stiff initial value problems, Berich Nr. 9, Inst. Fur Geometric und Practische Mathematik der RWTH Aachen, 1981.; P. Kaps, Rosenbrock-type methods, in: G. Dahlquist, R. Jeltsch, (Eds.), Numerical methods for stiff initial value problems, Berich Nr. 9, Inst. Fur Geometric und Practische Mathematik der RWTH Aachen, 1981. [6] He, J. H., Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., 178, 257-262 (1999) · Zbl 0956.70017 [7] He, J. H., The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. Math. Comput., 151, 287-292 (2004) · Zbl 1039.65052 [8] He, J. H., Application of homotopy perturbation method to nonlinear wave equations, Chaos Soliton. Fract., 26, 695-700 (2005) · Zbl 1072.35502 [9] He, J. H., Homotopy perturbation method for solving boundary value problems, Phys. Lett. A, 350, 87-88 (2006) · Zbl 1195.65207 [10] Biazar, J.; Ghazvini, H., Exact solutions for nonlinear Schrödinger equations by He’s homotopy perturbation method, Phys. Lett. A, 366, 79-84 (2007) · Zbl 1203.65207 [11] Ganji, D. D., The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer, Phys. Lett. A, 355, 337-341 (2006) · Zbl 1255.80026 [12] Odibat, Z.; Momani, S., Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order, Chaos. Soliton. Fract., 36, 167-174 (2008) · Zbl 1152.34311 [13] Cveticanin, L., Homotopy perturbation method for pure nonlinear differential equation, Chaos. Soliton. Fract., 30, 1221-1230 (2006) · Zbl 1142.65418 [14] Aminikhah, H.; Hemmatnezhad, M., An efficient method for quadratic Riccati differential equation, Commun. Nonlinear Sci. Numer. Simul., 15, 835-839 (2010) · Zbl 1221.65193 [15] Aminikhah, H.; Biazar, J., A new HPM for ordinary differential equations, Numer. Methods Partial Differ. Equat., 26, 480-489 (2009) · Zbl 1185.65129 [16] Yıldırım, A.; Koçak, H., Homotopy perturbation method for solving the space-time fractional advection-dispersion equation, Adv. Water Res., 32, 1711-1716 (2009) [17] Berberler, M. E.; Yıldırım, A., He’s homotopy perturbation method for solving the shock wave equation, Appl. Anal., 88, 997-1004 (2009) · Zbl 1172.76042 [18] Aminikhah, H., An analytical approximation for solving nonlinear Blasius equation by NHPM, Numer. Methods Partial Differ. Equat., 26, 1291-1299 (2010) · Zbl 1426.34032 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.