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Volumn 10, Issue 5, 2009, Pages 2633-2640

Convergence of the homotopy perturbation method for partial differential equations

Author keywords

Burgers' equations; Convergence sequence; Fourth order parabolic equations; Homotopy perturbation method; Partial differential equations; Schr dinger equations

Indexed keywords

APPROXIMATE SOLUTIONS; BURGERS' EQUATIONS; CONVERGENCE HYPOTHESIS; CONVERGENCE SEQUENCE; EXACT SOLUTIONS; FOURTH ORDER PARABOLIC EQUATIONS; FOURTH ORDERS; HOMOTOPY PERTURBATION METHOD; NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS; PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS;

EID: 64449088045     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.07.002     Document Type: Article
Times cited : (125)

References (24)
  • 1
    • 1242287587 scopus 로고    scopus 로고
    • The homotopy perturbation method for nonlinear oscillators with discontinuities
    • He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Applied Mathematics and Computation 151 (2004) 287-292
    • (2004) Applied Mathematics and Computation , vol.151 , pp. 287-292
    • He, J.H.1
  • 2
    • 18844426016 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to nonlinear wave equations
    • He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons and Fractals 26 (2005) 695-700
    • (2005) Chaos, Solitons and Fractals , vol.26 , pp. 695-700
    • He, J.H.1
  • 3
    • 30644460357 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving boundary value problems
    • He J.H. Homotopy perturbation method for solving boundary value problems. Physics Letters A 350 (2006) 87-88
    • (2006) Physics Letters A , vol.350 , pp. 87-88
    • He, J.H.1
  • 4
    • 18844391045 scopus 로고    scopus 로고
    • Limit cycle and bifurcation of nonlinear problems
    • He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos, Solitons and Fractals 26 3 (2005) 827-833
    • (2005) Chaos, Solitons and Fractals , vol.26 , Issue.3 , pp. 827-833
    • He, J.H.1
  • 6
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of homotopy technique and perturbation technique for nonlinear problems
    • He J.H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. International Journal of Non-Linear Mechanics 35 1 (2000) 37-43
    • (2000) International Journal of Non-Linear Mechanics , vol.35 , Issue.1 , pp. 37-43
    • He, J.H.1
  • 7
    • 3943092529 scopus 로고    scopus 로고
    • Comparison of homotopy perturbation method and homotopy analysis method
    • He J.H. Comparison of homotopy perturbation method and homotopy analysis method. Applied Mathematics and Computation 156 (2004) 527-539
    • (2004) Applied Mathematics and Computation , vol.156 , pp. 527-539
    • He, J.H.1
  • 8
    • 0037440579 scopus 로고    scopus 로고
    • Homotopy perturbation method: A new nonlinear analytical technique
    • He J.H. Homotopy perturbation method: A new nonlinear analytical technique. Applied Mathematics and Computation 135 (2003) 73-79
    • (2003) Applied Mathematics and Computation , vol.135 , pp. 73-79
    • He, J.H.1
  • 9
    • 34247862175 scopus 로고    scopus 로고
    • Exact solutions for nonlinear Schrödinger equations by He's homotopy perturbation method
    • Biazar J., and Ghazvini H. Exact solutions for nonlinear Schrödinger equations by He's homotopy perturbation method. Physics Letters A 366 (2007) 79-84
    • (2007) Physics Letters A , vol.366 , pp. 79-84
    • Biazar, J.1    Ghazvini, H.2
  • 10
    • 33646893481 scopus 로고    scopus 로고
    • The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer
    • Ganji D.D. The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer. Physics Letters A 355 (2006) 337-341
    • (2006) Physics Letters A , vol.355 , pp. 337-341
    • Ganji, D.D.1
  • 11
    • 32144434395 scopus 로고    scopus 로고
    • Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method
    • Abbasbandy S. Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method. Applied Mathematics and Computation 173 (2006) 493-500
    • (2006) Applied Mathematics and Computation , vol.173 , pp. 493-500
    • Abbasbandy, S.1
  • 12
    • 35348869861 scopus 로고    scopus 로고
    • Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order
    • Odibat Z., and Momani S. Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order. Chaos, Solitons and Fractals 36 1 (2008) 167-174
    • (2008) Chaos, Solitons and Fractals , vol.36 , Issue.1 , pp. 167-174
    • Odibat, Z.1    Momani, S.2
  • 13
    • 34548547253 scopus 로고    scopus 로고
    • Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane
    • Siddiqui A.M., Mahmood R., and Ghori Q.K. Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane. Chaos, Solitons and Fractals 35 1 (2008) 140-147
    • (2008) Chaos, Solitons and Fractals , vol.35 , Issue.1 , pp. 140-147
    • Siddiqui, A.M.1    Mahmood, R.2    Ghori, Q.K.3
  • 14
    • 33745852188 scopus 로고    scopus 로고
    • Homotopy-perturbation method for pure nonlinear differential equation
    • Cveticanin L. Homotopy-perturbation method for pure nonlinear differential equation. Chaos, Solitons and Fractals 30 (2006) 1221-1230
    • (2006) Chaos, Solitons and Fractals , vol.30 , pp. 1221-1230
    • Cveticanin, L.1
  • 15
    • 85120595985 scopus 로고    scopus 로고
    • He's homotopy perturbation method for solving system of Volterra integral equations of the second kind
    • in press
    • J. Biazar, H. Ghazvini, He's homotopy perturbation method for solving system of Volterra integral equations of the second kind, Chaos, Solitons and Fractals (in press)
    • Chaos, Solitons and Fractals
    • Biazar, J.1    Ghazvini, H.2
  • 16
    • 37449030301 scopus 로고    scopus 로고
    • Numerical solution for special non-linear Fredholm integral equation by HPM
    • Biazar J., and Ghazvini H. Numerical solution for special non-linear Fredholm integral equation by HPM. Applied Mathematics and Computation 195 (2008) 681-687
    • (2008) Applied Mathematics and Computation , vol.195 , pp. 681-687
    • Biazar, J.1    Ghazvini, H.2
  • 18
    • 0000332692 scopus 로고
    • On a quasilinear parabolic equations occurring in aerodynamics
    • Cole J.D. On a quasilinear parabolic equations occurring in aerodynamics. Quarterly of Applied Mathematics 9 (1951) 225-236
    • (1951) Quarterly of Applied Mathematics , vol.9 , pp. 225-236
    • Cole, J.D.1
  • 19
    • 32144458919 scopus 로고    scopus 로고
    • Acomparison between Cole-Hopf transformation and the decomposition method for solving Burgers' equations
    • Gorguis A. Acomparison between Cole-Hopf transformation and the decomposition method for solving Burgers' equations. Applied Mathematics and Computation 173 (2006) 126-136
    • (2006) Applied Mathematics and Computation , vol.173 , pp. 126-136
    • Gorguis, A.1
  • 20
    • 0037102860 scopus 로고    scopus 로고
    • Exact solutions for variable coefficients fourth-order parabolic partial differential equations in higher-dimensional Spaces
    • Wazwaz A.M. Exact solutions for variable coefficients fourth-order parabolic partial differential equations in higher-dimensional Spaces. Applied Mathematics and Computation 130 (2002) 415-424
    • (2002) Applied Mathematics and Computation , vol.130 , pp. 415-424
    • Wazwaz, A.M.1
  • 22
    • 0035949870 scopus 로고    scopus 로고
    • Analytical treatment for variable coefficients fourth-order parabolic partial differential equations
    • Wazwaz A.M. Analytical treatment for variable coefficients fourth-order parabolic partial differential equations. Applied Mathematics and Computation 123 (2001) 219-227
    • (2001) Applied Mathematics and Computation , vol.123 , pp. 219-227
    • Wazwaz, A.M.1
  • 23
    • 0038374490 scopus 로고    scopus 로고
    • Anew approach to the cubic Schrödinger equation: An application of the decomposition technique
    • Khuri S.A. Anew approach to the cubic Schrödinger equation: An application of the decomposition technique. Applied Mathematics and Computation 97 (1998) 251-254
    • (1998) Applied Mathematics and Computation , vol.97 , pp. 251-254
    • Khuri, S.A.1
  • 24
    • 34848888634 scopus 로고    scopus 로고
    • He's variational iteration method for fourth-order parabolic equations
    • Biazar J., and Ghazvini H. He's variational iteration method for fourth-order parabolic equations. Computers and Mathematics with Applications 54 (2007) 1047-1054
    • (2007) Computers and Mathematics with Applications , vol.54 , pp. 1047-1054
    • Biazar, J.1    Ghazvini, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.