Linearized perturbation method for stochastic analysis of a rill erosion model. (English) Zbl 1164.86002

Summary: The linearization and correction method (LCM) proposed by He is a simple and effective perturbation technique to solve nonlinear equations. To analyze the random properties of rill erosion model, a new stochastic perturbation technique called linearized perturbation method is developed by combining the traditional stochastic perturbation method with the LCM. Comparisons between the numerical results obtained by the linearized perturbation method and those obtained by Monte Carlo method indicated an excellent agreement. However, the calculation efficiency of the linearized perturbation method is higher.


86A04 General questions in geophysics
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[1] Lei, T. W.; Nearing, M. A.; Haghighi, K.; Bralts, V. F., Rill erosion and morphological evolution: a simulation model, Water Resour. Res., 34, 11, 3157-3168 (1998)
[2] Zhang, S. W.; Ellingwood, B.; Corotis, R.; Zhang, J., Direct integration method for stochastic finite element analysis of nonlinear dynamic response, Struct. Eng. Mech., 3, 3, 273-287 (1995)
[3] Zhang, S. W.; Datta, A. K.; Ni, H. T., The stochastic element method for analyzing conduction heat transfer in foods, Trans. CSAE, 11, 2, 143-148 (1995)
[4] He, J.-H., Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B, 20, 10, 1141-1199 (2006) · Zbl 1102.34039
[5] He, J.-H., Linearization and correction method for nonlinear problems, Appl. Math. Mech., 23, 3, 241-247 (2002) · Zbl 1028.70015
[6] He, J.-H., Homotopy perturbation technique, Comput. Method Appl. Mech. Eng., 178, 3/4, 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., Homotopy-perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear Sci. Numer. Simulat. Nonlinear, 6, 207-208 (2005) · Zbl 1401.65085
[9] He, J.-H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Non-Linear Mech., 35, 1, 37-43 (2000) · Zbl 1068.74618
[10] He, J.-H., Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput., 135, 73-79 (2003) · Zbl 1030.34013
[11] He, J.-H., Application of homotopy perturbation method to nonlinear wave equations, Chaos Soliton Fract., 26, 695-700 (2005) · Zbl 1072.35502
[12] He, J.-H., Periodic solutions and bifurcations of delay-differential equations, Phys. Lett. A, 347, 228-230 (2005) · Zbl 1195.34116
[13] El-Shahed, M., Application of He’s homotopy-perturbation method to Volterra’s integro-differential equation, Int. J. Nonlinear Sci. Numer. Simulat. Nonlinear, 6, 163-168 (2005) · Zbl 1401.65150
[14] Cveticanin, L., The homotopy-perturbation method applied for solving complex-values differential equations with strong cubic nonlinearity, J. Sound Vibration, 285, 1171-1179 (2005) · Zbl 1238.65085
[15] He, J.-H., An approximate solution technique depending upon an artificial parameter, Commun. Nonlinear Sci. Numer. Simulat., 32, 92-97 (1998) · Zbl 0921.35009
[16] He, J.-H., Variational iteration method: a kind of nonlinear analytical technique: some examples, Int. Non-Linear Mech., 344, 699-708 (1999) · Zbl 1342.34005
[17] He, J.-H., Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput., 114, 2,3, 115-123 (2000) · Zbl 1027.34009
[18] He, J.-H.; Wu, X.-H., Construction of solitary solution and compaction-like solution by variational iteration method, Chaos Soliton Fract., 29, 1, 108-113 (2006) · Zbl 1147.35338
[19] Abdou, M. A.; Soliman, A. A., Variational iteration method for solving Burgers’ and coupled Burgers’ equations, J. Comput. Appl. Math., 181, 245-251 (2005) · Zbl 1072.65127
[20] Soliman, A. A., A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations, Chaos Soliton Fract., 29, 2, 294-302 (2006) · Zbl 1099.35521
[21] Abulwafa, E. M.; Abdou, M. A.; Mahmoud, A. A., The solution of nonlinear coagulation problem with mass loss, Chaos Soliton Fract., 29, 2, 313-330 (2006) · Zbl 1101.82018
[22] Momani, S.; Abuasad, S., Application of He’s variational iteration method to Helmholtz equation, Chaos Soliton Fract., 27, 5, 1119-1123 (2006) · Zbl 1086.65113
[23] Bildik, N.; Konuralp, A., The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations, Int. J. Nonlinear Sci., 7, 1, 65-70 (2006) · Zbl 1401.35010
[24] Odibat, Z. M.; Momani, S., Application of variational iteration method to Nonlinear differential equations of fractional order, Int. J. Nonlinear Sci., 7, 1, 27-34 (2006) · Zbl 1401.65087
[25] Nearing, M. A., A probabilistic model of soil detachment by shallow turbulent flow, Trans. ASAE, 34, 81-85 (1991)
[26] Misra, R. K.; Rose, C. W., Application and sensitivity analysis of process based erosion model GUEST, Eur. J. Soil Sci., 47, 593-604 (1996)
[27] Morgan, R. P.C., The European soil erosion model: an update on its structure and research base, (Rickson, R. J., Conserving Soil Resources. Conserving Soil Resources, European Perspectives (1995), CAB International: CAB International Oxon, UK), 286-299
[28] Morgan, R. P.C.; Quinton, J. N.; Rickson, R. J., EUROSEM Documentation Manual (1992), Silsoe College: Silsoe College Silsoe, Bedford, UK
[29] Wang, D.; Wei, G., The study of quasi-wavelets based numerical method applied to Burgers’ equations, Appl. Math. Mech., 21, 10, 991-1001 (2000)
[30] Nearing, M. A.; Foster, G. R.; Lane, L. J.; Finkner, S. C., A process-based soil erosion model for USDA-water erosion prediction project technology, Trans. ASAE, 32, 1587-1593 (1989)
[31] Nearing, M. A.; Lane, L. J.; Alberts, E. E.; Laflen, J. M., Prediction technology for soil erosion by water: status and research needs, Soil Sci. Soc. Am. J, 54, 1702-1711 (1990)
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