zbMATH — the first resource for mathematics

Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Variational iteration method and homotopy perturbation method for nonlinear evolution equations. (English) Zbl 1141.65384
Summary: The variational iteration and homotopy perturbation methods are applied to various evolution equations. To assess the accuracy of the solutions, we compare the results with the exact solutions, revealing that both methods are capable of solving effectively a large number of nonlinear differential equations with high accuracy.

MSC:
 65M70 Spectral, collocation and related methods (IVP of PDE) 35L75 Nonlinear hyperbolic PDE of higher $(>2)$ order
Full Text:
References:
 [1] Kaya, D.: An explicit and numerical solutions of some fifth-order KdV equation by decomposition method. Applied mathematics and computation 144, 353-363 (2003) · Zbl 1024.65096 [2] Al-Khaled, K.: Approximate wave solutions for generalized benjamin--bona--Mahony--Burgers equations. Applied mathematics and computation 171, 281-292 (2005) · Zbl 1084.65097 [3] D.D. Ganji, The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer, Physics Letters A (in press) · Zbl 1255.80026 [4] D.D. Ganji, Solitary wave solutions for a generalized Hirota--Satsuma coupled KdV equation by homotopy perturbation method, Physics Letters A (in press) · Zbl 1160.35517 [5] Ganji, D. D.: Assessment of homotopy--perturbation and perturbation methods in heat radiation equations. International communications in heat and mass transfer 33, No. 3, 391-400 (2006) [6] C. Jin, M. Liu, A new modification of Adomian decomposition method for solving a kind of evolution equation, 169 (2005) 953--962 · Zbl 1121.65355 [7] Adomian, G.: A review of the decomposition method in applied mathematics. Journal of mathematical analysis and applications 135, 501-544 (1988) · Zbl 0671.34053 [8] He, J. H.: Some asymptotic methods for strongly nonlinear equations. International journal of modern physics B 20, 1141-1199 (2006) · Zbl 1102.34039 [9] He, J. H.: Non-perturbative methods for strongly nonlinear problems. (2006) [10] He, J. H.: Homotopy perturbation technique. Computer methods in applied mechanics and engineering 178, No. 3-4, 257-262 (1999) · Zbl 0956.70017 [11] He, J. H.: A coupling method of a homotopy technique and a perturbation technique for non-linear problems. International journal of non-linear mechanics 35, No. 1, 37-43 (2000) · Zbl 1068.74618 [12] He, J. H.: New interpretation of homotopy perturbation method. International journal of modern physics B 20, 2561-2568 (2006) [13] He, J. H.: Variational iteration method--a kind of nonlinear analytical technique: some examples. International journal of non-linear mechanics 34, No. 4, 699-708 (1999) · Zbl 05137891 [14] He, J. H.: Approximate analytical solution for seepage with fractional derivatives in porous media. Computational methods in applied mechanics and engineering 167, 57-68 (1998) · Zbl 0942.76077 [15] He, J. H.: Approximate solution of nonlinear differential equations with convolution product nonlinearities. Computational methods in applied mechanics and engineering 167, 69-73 (1998) · Zbl 0932.65143 [16] He, J. H.: Homotopy perturbation method: A new nonlinear analytical technique. Applied mathematics and computation 135, No. 1, 73-79 (2003) · Zbl 1030.34013 [17] He, J. H.: The homotopy perturbation method for nonlinear oscillators with discontinuities. Applied mathematics and computation 151, No. 1, 287-292 (2004) · Zbl 1039.65052 [18] He, J. H.: Periodic solutions and bifurcations of delay-differential equations. Physics letters A 347, No. 4--6, 228-230 (2005) · Zbl 1195.34116 [19] He, J. H.: Application of homotopy perturbation method to nonlinear wave equations. Chaos, solitons and fractals 26, No. 3, 695-700 (2005) · Zbl 1072.35502 [20] He, J. H.: Limit cycle and bifurcation of nonlinear problems. Chaos, solitons and fractals 26, No. 3, 827-833 (2005) · Zbl 1093.34520 [21] He, J. H.: Homotopy perturbation method for bifurcation of nonlinear problems. International journal of nonlinear sciences and numerical simulation 6, No. 2, 207-208 (2005) [22] He, J. H.: Homotopy perturbation method for solving boundary value problems. Physics letters A 350, No. 1--2, 87-88 (2006) · Zbl 1195.65207 [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. International journal of nonlinear sciences and numerical simulation 7, No. 1, 65-70 (2006) · Zbl 1115.65365 [24] He, J. H.; Wu, X. H.: Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, solitons and fractals 29, No. 1, 108-113 (2006) · Zbl 1147.35338 [25] He, J. H.: Variational iteration method for autonomous ordinary differential systems. Applied mathematics and computation 114, No. 2--3, 115-123 (2000) · Zbl 1027.34009