메뉴 건너뛰기




Volumn 5, Issue 1, 2010, Pages

Revisiting reaction-diffusion process in a porous catalyst: Improving the adomian solution

Author keywords

Adomian decomposition; catalyst; orthogonal polynomials; reaction diffusion equation

Indexed keywords

ADOMIAN DECOMPOSITION; ADOMIAN METHOD; ADOMIAN POLYNOMIALS; ANALYTICAL EXPRESSIONS; ORTHOGONAL POLYNOMIAL; ORTHOGONAL POLYNOMIALS; POROUS CATALYSTS; REACTION-DIFFUSION EQUATION; REACTION-DIFFUSION PROCESS;

EID: 77955926528     PISSN: 19342659     EISSN: None     Source Type: Journal    
DOI: 10.2202/1934-2659.1465     Document Type: Article
Times cited : (6)

References (37)
  • 1
    • 38649139314 scopus 로고    scopus 로고
    • Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method
    • DOI 10.1016/j.cej.2007.03.022, PII S1385894707001672
    • Abbasbandy, S. (2008) Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method. Chem. Eng. J. 136(2-3), 144-150. (Pubitemid 351173865)
    • (2008) Chemical Engineering Journal , vol.136 , Issue.2-3 , pp. 144-150
    • Abbasbandy, S.1
  • 2
    • 0037420925 scopus 로고    scopus 로고
    • A mathematical model of Adomian polynomials
    • Abdelwahid, F. (2003) A mathematical model of Adomian polynomials. Appl. Math. Comput. 141, 447-453.
    • (2003) Appl. Math. Comput. , vol.141 , pp. 447-453
    • Abdelwahid, F.1
  • 6
    • 34249806325 scopus 로고    scopus 로고
    • Derivation of the Adomian decomposition method using the homotopy analysis method
    • DOI 10.1016/j.amc.2006.12.074, PII S0096300307000227
    • Allan, F.M. (2007) Derivation of Adomian decomposition method using the homotopy analysis method. Appl. Math. Comput. 190, 6-14. (Pubitemid 46856640)
    • (2007) Applied Mathematics and Computation , vol.190 , Issue.1 , pp. 6-14
    • Allan, F.M.1
  • 8
    • 2642580023 scopus 로고    scopus 로고
    • Restarted Adomian method for integral equations
    • Babolian, E., Javadi. S., Sadeghi, H. (2004) Restarted Adomian method for integral equations. Appl. Math. Comput. 153, 353-359.
    • (2004) Appl. Math. Comput. , vol.153 , pp. 353-359
    • Babolian, E.1    Javadi., S.2    Sadeghi, H.3
  • 9
    • 0037457727 scopus 로고    scopus 로고
    • An alternate algorithm for computing Adomian polynomials in special cases
    • Biazar, J., Babolian, E., Kember, G., Nouri, A., Isalm, R. (2003) An alternate algorithm for computing Adomian polynomials in special cases. Appl. Math. Comput. 138, 523-529.
    • (2003) Appl. Math. Comput. , vol.138 , pp. 523-529
    • Biazar, J.1    Babolian, E.2    Kember, G.3    Nouri, A.4    Isalm, R.5
  • 10
    • 0141920794 scopus 로고    scopus 로고
    • Solution of the system of ordinary differential equations by Adomian decomposition method
    • Biazar, J., Babolian, E., Isalm, R. (2004) Solution of the system of ordinary differential equations by Adomian decomposition method. Appl. Math. Comput. 147, 713-719.
    • (2004) Appl. Math. Comput. , vol.147 , pp. 713-719
    • Biazar, J.1    Babolian, E.2    Isalm, R.3
  • 11
    • 0037174262 scopus 로고    scopus 로고
    • The decomposition method for ordinary differential equations with discontinuities
    • DOI 10.1016/S0096-3003(01)00142-4, PII S0096300301001424
    • Casasús, L., Al-Hayani, W. (2002) The decomposition method for ordinary differential equations with discontinuities. Appl. Math. Comput. 131, 245-251. (Pubitemid 34813483)
    • (2002) Applied Mathematics and Computation , vol.131 , Issue.2-3 , pp. 245-251
    • Casasus, L.1    Al-Hayani, W.2
  • 12
    • 0042012869 scopus 로고    scopus 로고
    • Symbolic implementation of the algorithm for calculating Adomian polynomials
    • Choi, H.W., Shin, J.G. (2003) Symbolic implementation of the algorithm for calculating Adomian polynomials. Appl. Math. Comput. 146, 257-271.
    • (2003) Appl. Math. Comput. , vol.146 , pp. 257-271
    • Choi, H.W.1    Shin, J.G.2
  • 13
    • 79952463525 scopus 로고    scopus 로고
    • A reliable treatment of a homotopy analysis method for two-dimensional viscous flow in a rectangular domain bounded by two moving porous walls
    • available online
    • Dinarvand, Saeed, Rashidi. M.M. (2009) A reliable treatment of a homotopy analysis method for two-dimensional viscous flow in a rectangular domain bounded by two moving porous walls. Nonlinear Anal.: Real World Appl. (available online).
    • (2009) Nonlinear Anal.: Real World Appl.
    • Saeed, D.1    Rashidi., M.M.2
  • 16
    • 18844412668 scopus 로고    scopus 로고
    • Approximate expression for the effectiveness factor estimation and a simple numerical method for concentration profile calculation in porous catalyst
    • DOI 10.1016/j.cej.2005.03.012, PII S1385894705001257
    • Gottifredi, J. C., Gonzo, E. E. (2005) Approximate expression for the effectiveness factor estimation and a simple numerical method for concentration profile calculation in porous catalyst. Chem. Eng. J. 109, 83-87. (Pubitemid 40697245)
    • (2005) Chemical Engineering Journal , vol.109 , Issue.1-3 , pp. 83-87
    • Gottifredi, J.C.1    Gonzo, E.E.2
  • 17
    • 58749094806 scopus 로고    scopus 로고
    • Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method
    • Hasan, Y.Q., Zhu, L.M. (2009) Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method. Commun. Nonlinear Sci. Numer. Simul. 14, 2592-2596.
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 2592-2596
    • Hasan, Y.Q.1    Zhu, L.M.2
  • 18
    • 33645877651 scopus 로고    scopus 로고
    • Adomian decomposition method with Chebyshev polynomilas
    • Hosseini, M.M. (2006) Adomian decomposition method with Chebyshev polynomilas. Appl. Math. Comput. 175, 1685-1693.
    • (2006) Appl. Math. Comput. , vol.175 , pp. 1685-1693
    • Hosseini, M.M.1
  • 19
    • 3843147199 scopus 로고    scopus 로고
    • A reliable method for the numerical solution of the kinetics problems
    • Kaya, D. (2004) A reliable method for the numerical solution of the kinetics problems. Appl. Math. Comput. 156, 261-270.
    • (2004) Appl. Math. Comput. , vol.156 , pp. 261-270
    • Kaya, D.1
  • 20
    • 38949187527 scopus 로고    scopus 로고
    • Remark on modifications of Adomian decomposition method
    • DOI 10.1016/j.amc.2007.07.058, PII S0096300307007655
    • Layeni, O.P. (2008) Remark on modifications of Adomian decomposition method. Appl. Math. Comput. 197, 167-171. (Pubitemid 351222671)
    • (2008) Applied Mathematics and Computation , vol.197 , Issue.1 , pp. 167-171
    • Layeni, O.P.1
  • 21
    • 33846625552 scopus 로고    scopus 로고
    • A nonlinear reaction-diffusion process using the Adomian decomposition method
    • DOI 10.1016/j.icheatmasstransfer.2006.11.005, PII S0735193306002156
    • Lesnic, D. (2007) A nonlinear reaction-diffusion process using the Adomian decomposition method. Int. Commun. Heat Mass Tr. 34, 129-135. (Pubitemid 46173173)
    • (2007) International Communications in Heat and Mass Transfer , vol.34 , Issue.2 , pp. 129-135
    • Lesnic, D.1
  • 22
    • 63349091089 scopus 로고    scopus 로고
    • Adomian's decomposition method and homotopy perturbation method in solving nonlinear equations
    • Li, J. (2009) Adomian's decomposition method and homotopy perturbation method in solving nonlinear equations. J. Comput. Appl. Math., 228(1), 168.
    • (2009) J. Comput. Appl. Math. , vol.228 , Issue.1 , pp. 168
    • Li, J.1
  • 23
    • 59149087485 scopus 로고    scopus 로고
    • Adomian decomposition method with orthogonal polynomials: Legendre polynomials
    • Liu, Y. (2009) Adomian decomposition method with orthogonal polynomials: Legendre polynomials. Math. Comput. Model. 49, 1268.
    • (2009) Math. Comput. Model. , vol.49 , pp. 1268
    • Liu, Y.1
  • 24
    • 50649122301 scopus 로고    scopus 로고
    • Exact analytical solution of a nonlinear reaction-diffusion model in porous catalysts
    • Magyari, E. (2008) Exact analytical solution of a nonlinear reaction-diffusion model in porous catalysts, Chem. Eng. J. 143, 167-171.
    • (2008) Chem. Eng. J. , vol.143 , pp. 167-171
    • Magyari, E.1
  • 25
    • 25144469362 scopus 로고    scopus 로고
    • The decomposition method for stiff systems of ordinary differential equations
    • DOI 10.1016/j.amc.2004.06.134, PII S0096300304005429
    • Mahmood, A.S., Casasús, L., Al-Hayani, W. (2005) The decomposition method for stiff systems of ordinary differential equations. Appl. Math. Comput. 167, 964-975. (Pubitemid 41344802)
    • (2005) Applied Mathematics and Computation , vol.167 , Issue.2 , pp. 964-975
    • Mahmood, A.S.1    Casasus, L.2    Al-Hayani, W.3
  • 26
    • 79952474697 scopus 로고    scopus 로고
    • Symmetry analysis for the nonlinear model of diffusion and reaction in porous catalysts
    • available online
    • Moitsheki, R.J., Hayat, T., Malik, M.Y., Mahomeda, F.M. (2009) Symmetry analysis for the nonlinear model of diffusion and reaction in porous catalysts. Nonlinear Anal.: Real World Appl. (available online).
    • (2009) Nonlinear Anal.: Real World Appl.
    • Moitsheki, R.J.1    Hayat, T.2    Malik, M.Y.3    Mahomeda, F.M.4
  • 27
    • 0012249579 scopus 로고
    • Adomian's method of decomposition: Critical review and examples of failure
    • Nelson, P. (1988) Adomian's method of decomposition: critical review and examples of failure. J. Comput. Appl. Math. 23, 389-393.
    • (1988) J. Comput. Appl. Math. , vol.23 , pp. 389-393
    • Nelson, P.1
  • 28
    • 0030187555 scopus 로고    scopus 로고
    • Adomian's polynomials for nonlinear operators
    • Seng, V., Abbaoui, K., Cherruault, Y. (1996) Adomian's polynomials for nonlinear operators. Math. Comput. Model. 24(1), 59-65.
    • (1996) Math. Comput. Model. , vol.24 , Issue.1 , pp. 59-65
    • Seng, V.1    Abbaoui, K.2    Cherruault, Y.3
  • 29
    • 2942738809 scopus 로고    scopus 로고
    • Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by the decomposition method
    • DOI 10.1016/S1385-8947(03)00060-3, PII S1385894703000603
    • Sun, Y., Liu, S., Scott, K. (2004) Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method. Chem. Eng. J. 102, 1-10. (Pubitemid 38790901)
    • (2004) Chemical Engineering Journal , vol.102 , Issue.1 , pp. 1-10
    • Sun, Y.-P.1    Liu, S.-B.2    Keith, S.3
  • 30
    • 85024307490 scopus 로고
    • Relation between catalytic activity and size of particle
    • Thiele, E. W. (1939) Relation between catalytic activity and size of particle, Ind. Eng. Chem. 31, 916-920.
    • (1939) Ind. Eng. Chem. , vol.31 , pp. 916-920
    • Thiele, E.W.1
  • 31
    • 64049093900 scopus 로고    scopus 로고
    • Adomian decomposition method by Legendre polynomials
    • Tien, W., Chen, C. (2007) Adomian decomposition method by Legendre polynomials. Chaos, Solitons Fractals. 39(5), 2093-2101.
    • (2007) Chaos, Solitons Fractals. , vol.39 , Issue.5 , pp. 2093-2101
    • Tien, W.1    Chen, C.2
  • 33
    • 58349100241 scopus 로고    scopus 로고
    • Variational iteration method for a nonlinear reaction-diffusion process
    • Article A37
    • Wang, Shu-Qiang, He, J.H. (2008) Variational iteration method for a nonlinear reaction-diffusion process. Int. J. Chem. Reac. Eng. 6, Article A37.
    • (2008) Int. J. Chem. Reac. Eng. , vol.6
    • Shu-Qiang, W.1    He, J.H.2
  • 34
    • 0002566545 scopus 로고    scopus 로고
    • A comparison between Adomian decomposition method and Taylor series method in the series solutions
    • PII S0096300397101278
    • Wazwaz, A. (1998) A comparison between Adomian decomposition method and Taylor series method in the series solutions. Appl. Math. Comput. 97, 37-44. (Pubitemid 128682500)
    • (1998) Applied Mathematics and Computation , vol.97 , Issue.1 , pp. 37-44
    • Wazwaz, A.-M.1
  • 35
    • 0034276401 scopus 로고    scopus 로고
    • Approximate solutions to boundary value problems of higher order by the decomposition method
    • Wazwaz, A. (2000a) Approximate solutions to boundary value problems of higher order by the decomposition method. Comput. Math. Appl. 40, 679-691.
    • (2000) Comput. Math. Appl. , vol.40 , pp. 679-691
    • Wazwaz, A.1
  • 36
    • 0347450513 scopus 로고    scopus 로고
    • A new algorithm for calculating Adomian polynomials for nonlinear operators
    • Wazwaz, A. (2000b) A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl. Math. Comput. 111, 53-69.
    • (2000) Appl. Math. Comput. , vol.111 , pp. 53-69
    • Wazwaz, A.1
  • 37
    • 0001450192 scopus 로고
    • Reaction rate and selectivity in catalyst pores
    • Wheeler, A. (1955) Reaction rate and selectivity in catalyst pores, Catalysis 2, 105-165.
    • (1955) Catalysis , vol.2 , pp. 105-165
    • Wheeler, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.