zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method. (English) Zbl 1165.65377
Summary: The homotopy perturbation method proposed by Ji-Huan He is applied to solve both linear and nonlinear boundary value problems for fourth-order integro-differential equations. The analysis is accompanied by numerical examples. The results show that the homotopy perturbation method is of high accuracy, more convenient and efficient for solving integro-differential equations.

65L99Numerical methods for ODE
45J05Integro-ordinary differential equations
Full Text: DOI
[1] P.K. Kythe, P. Puri, Computational methods for linear integral equations, University of New Orleans, New Orleans, 1992 · Zbl 1023.65134
[2] Wazwaz, A. M.: A comparison study between the modified decomposition method and the traditional methods, Applied mathematics and computation 181, 1703-1712 (2006) · Zbl 1105.65128 · doi:10.1016/j.amc.2006.03.023
[3] Avudainayagam, A.; Vani, C.: Wavelet-Galerkin method for integro-differential equations, Applied numerical mathematics 32, 247-254 (2000) · Zbl 0955.65100 · doi:10.1016/S0168-9274(99)00026-4
[4] Rashed, M. T.: Lagrange interpolation to compute the numerical solutions of differential, integral and integro-differential equations, Applied mathematics and computation 151, 869-878 (2004) · Zbl 1048.65133 · doi:10.1016/S0096-3003(03)00543-5
[5] Hosseini, S. M.; Shahmorad, S.: Tau numerical solution of Fredholm integro-differential equations with arbitrary polynomial bases, Applied mathematical modeling 27, 145-154 (2003) · Zbl 1047.65114 · doi:10.1016/S0307-904X(02)00099-9
[6] El-Sayed, S. M.; Abdel-Aziz, M. R.: A comparison of Adomian’s decomposition method and wavelet-Galerkin method for integro-differential equations, Applied mathematics and computation 136, 151-159 (2003) · Zbl 1023.65149 · doi:10.1016/S0096-3003(02)00024-3
[7] Wazwaz, A. M.: A reliable algorithm for solving boundary value problems for higher-order integro-differential equations, Applied mathematics and computation 118, 327-342 (2001) · Zbl 1023.65150 · doi:10.1016/S0096-3003(99)00225-8
[8] Hashim, I.: Adomian decomposition method for solving BVPs for fourth-order integro-differential equations, Journal of computational and applied mathematics 193, 658-664 (2006) · Zbl 1093.65122 · doi:10.1016/j.cam.2005.05.034
[9] Maleknejad, K.; Mahmoudi, Y.: Taylor polynomial solution of high-order nonlinear Volterra--Fredholm integro-differential equations, Applied mathematics and computation 145, 641-653 (2003) · Zbl 1032.65144 · doi:10.1016/S0096-3003(03)00152-8
[10] Maleknejad, K.; Mirzaee, F.; Abbasbandy, S.: Solving linear integro-differential equations system by using rationalized Haar function method, Applied mathematics and computation 155, 317-328 (2005) · Zbl 1056.65144 · doi:10.1016/S0096-3003(03)00778-1
[11] Arikoglu, A.; Ozkol, I.: Solution of boundary value problems for integro-differential equations by using differential transform method, Applied mathematics and computation 168, 1145-1158 (2005) · Zbl 1090.65145 · doi:10.1016/j.amc.2004.10.009
[12] Sweilam, N. H.: Fourth order integro-differential equations using variational iteration method, Computers and mathematics with applications 54, 1086-1091 (2007) · Zbl 1141.65399 · doi:10.1016/j.camwa.2006.12.055
[13] He, J. H.: Variational iteration method: new development and applications, Computers and mathematics with applications 54, 881-894 (2007) · Zbl 1141.65372 · doi:10.1016/j.camwa.2006.12.083
[14] He, J. H.: Homotopy perturbation technique, Computational methods in applied mechanics and engineering 178, 257-262 (1999) · Zbl 0956.70017
[15] 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, 37-43 (2000) · Zbl 1068.74618 · doi:10.1016/S0020-7462(98)00085-7
[16] He, J. H.: Comparison of homotopy perturbation method and homotopy analysis method, Applied mathematics and computation 156, 527-539 (2004) · Zbl 1062.65074 · doi:10.1016/j.amc.2003.08.008
[17] He, J. H.: Homotopy perturbation method: A new nonlinear analytical technique, Applied mathematics and computation 135, 73-79 (2003) · Zbl 1030.34013 · doi:10.1016/S0096-3003(01)00312-5
[18] He, J. H.: The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied mathematics and computation 151, 287-292 (2004) · Zbl 1039.65052 · doi:10.1016/S0096-3003(03)00341-2
[19] He, J. H.: Application of homotopy perturbation method to nonlinear wave equations, Chaos,Solitons and fractals 26, 695-700 (2004) · Zbl 1072.35502 · doi:10.1016/j.chaos.2005.03.006
[20] Cveticanin, L.: Homotopy--perturbation method for pure nonlinear differential equation, Chaos solitons and fractals 30, 1221-1230 (2006) · Zbl 1142.65418 · doi:10.1016/j.chaos.2005.08.180
[21] Ganji, D. D.; Rafei, M.: Solitary wave solutions for a generalized Hirota--satsuma coupled KdV equation by homotopy perturbation method, Physics letters A 356, 131-137 (2006) · Zbl 1160.35517 · doi:10.1016/j.physleta.2006.03.039
[22] Siddiqui, A. M.; Mahmood, R.; Ghori, Q. K.: Some exact solutions for the thin film flow of a PTT fluid, Physics letter A 352, 404-410 (2006) · Zbl 1187.76622
[23] Öziş, T.; Yıldırım, A.: A note on he’s homotopy perturbation method for van der Pol oscillator with very strong nonlinearity, Chaos,Solitons and fractals 34, 989-991 (2007)
[24] Öziş, T.; Yıldırım, A.: Traveling wave solution of Korteweg--de Vries equation using he’s homotopy perturbation method, International journal of nonlinear science and numerical simulation 8, 239-242 (2007)
[25] Öziş, T.; Yıldırım, A.: A comparative study of he’s homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities, International journal of nonlinear science and numerical simulation 8, 243-248 (2007)
[26] Yıldırım, A.; Öziş, T.: Solutions of singular ivps of Lane--Emden type by homotopy perturbation method, Physics letters A 369, 70-76 (2007) · Zbl 1209.65120 · doi:10.1016/j.physleta.2007.04.072