메뉴 건너뛰기




Volumn 68, Issue 1-2, 2012, Pages 17-21

Analytic solution for a nonlinear chemistry system of ordinary differential equations

Author keywords

Analytic solution; Nonlinear chemistry system; Ordinary differential equations; Symbolic computation

Indexed keywords

ANALYTIC SOLUTION; NON-LINEAR CHEMISTRY; POTASSIUM PERMANGANATE; REACTION MECHANISM; SYMBOLIC COMPUTATION; SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS;

EID: 84858701688     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-011-0200-6     Document Type: Article
Times cited : (7)

References (31)
  • 1
    • 34748888282 scopus 로고    scopus 로고
    • A generalized auxiliary equation method and its application to (2+1) -dimensional Korteweg-de Vries equations
    • DOI 10.1016/j.camwa.2006.12.046, PII S0898122107002684, Variational Iteration Method for Nonlinear Problems
    • S. Zhang 2007 A generalized auxiliary equation method and its application to (2+1)-dimensional Korteweg-de Vries equations Comput. Math. Appl. 54 1028 1038 2395641 1143.35363 10.1016/j.camwa.2006.12.046 (Pubitemid 47488817)
    • (2007) Computers and Mathematics with Applications , vol.54 , Issue.7-8 , pp. 1028-1038
    • Zhang, S.1
  • 2
    • 34548107381 scopus 로고    scopus 로고
    • Soliton solutions and a Bäcklund transformation for a generalized nonlinear Schrödinger equation with variable coefficients from optical fiber communications
    • 2353015 1128.35385 10.1016/j.jmaa.2007.03.017
    • X. Lü H.W. Zhu X.H. Meng Z.C. Yang B. Tian 2007 Soliton solutions and a Bäcklund transformation for a generalized nonlinear Schrödinger equation with variable coefficients from optical fiber communications J. Math. Anal. Appl. 336 1305 1315 2353015 1128.35385 10.1016/j.jmaa.2007.03.017
    • (2007) J. Math. Anal. Appl. , vol.336 , pp. 1305-1315
    • Lü, X.1    Zhu, H.W.2    Meng, X.H.3    Yang, Z.C.4    Tian, B.5
  • 3
    • 44449104927 scopus 로고    scopus 로고
    • Clothing up DNA for all seasons: Histone chaperones and nucleosome assembly pathways
    • 10.1016/j.febslet.2008.03.006
    • W. Rocha A. Verreault 2008 Clothing up DNA for all seasons: Histone chaperones and nucleosome assembly pathways FEBS Lett. 582 1938 1949 10.1016/j.febslet.2008.03.006
    • (2008) FEBS Lett. , vol.582 , pp. 1938-1949
    • Rocha, W.1    Verreault, A.2
  • 4
    • 14944372079 scopus 로고    scopus 로고
    • A nonlinear parabolic system arising in damage mechanics under chemical aggression
    • DOI 10.1016/j.na.2004.07.056, PII S0362546X0400567X
    • C. Nitsch 2005 A nonlinear parabolic system arising in damage mechanics under chemical aggression Nonlinear Anal. 61 695 713 2130060 1063.35072 10.1016/j.na.2004.07.056 (Pubitemid 40370489)
    • (2005) Nonlinear Analysis, Theory, Methods and Applications , vol.61 , Issue.5 , pp. 695-713
    • Nitsch, C.1
  • 6
    • 26844436587 scopus 로고    scopus 로고
    • Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations
    • DOI 10.1016/j.amc.2004.10.066, PII S0096300304008689
    • H.Q. Wang 2005 Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations Appl. Math. Comput. 170 17 35 2177202 1082.65570 10.1016/j.amc.2004.10.066 (Pubitemid 41460449)
    • (2005) Applied Mathematics and Computation , vol.170 , Issue.1 , pp. 17-35
    • Wang, H.1
  • 7
    • 0002297925 scopus 로고
    • Reliability of the finite element method for calculating free edge stresses in composite laminates
    • 10.1016/0045-7949(82)90030-X
    • J.D. Whitcomb I.S. Raju J.G. Goree 1982 Reliability of the finite element method for calculating free edge stresses in composite laminates Comput. Struct. 15 23 37 10.1016/0045-7949(82)90030-X
    • (1982) Comput. Struct. , vol.15 , pp. 23-37
    • Whitcomb, J.D.1    Raju, I.S.2    Goree, J.G.3
  • 8
    • 1842505268 scopus 로고    scopus 로고
    • Exact and numerical traveling wave solutions for nonlinear coupled equations using symbolic computation
    • 2052457 1048.65096 10.1016/S0096-3003(03)00535-6
    • D. Kaya E.I. Inan 2004 Exact and numerical traveling wave solutions for nonlinear coupled equations using symbolic computation Appl. Math. Comput. 151 775 787 2052457 1048.65096 10.1016/S0096-3003(03)00535-6
    • (2004) Appl. Math. Comput. , vol.151 , pp. 775-787
    • Kaya, D.1    Inan, E.I.2
  • 9
    • 30344475545 scopus 로고    scopus 로고
    • Construction of solitary solution and compacton-like solution by variational iteration method
    • DOI 10.1016/j.chaos.2005.10.100, PII S0960077905010799
    • J.H. He X.H. Wu 2006 Construction of solitary solution and compacton-like solution by variational iteration method Chaos Solitons Fractals 29 108 113 2213340 1147.35338 10.1016/j.chaos.2005.10.100 (Pubitemid 43063201)
    • (2006) Chaos, Solitons and Fractals , vol.29 , Issue.1 , pp. 108-113
    • He, J.-H.1    Wu, X.-H.2
  • 10
    • 30644460357 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving boundary value problems
    • DOI 10.1016/j.physleta.2005.10.005, PII S0375960105015434
    • J.H. He 2006 Homotopy perturbation method for solving boundary value problems Phys. Lett. A 350 87 88 2199322 1195.65207 10.1016/j.physleta.2005.10. 005 (Pubitemid 43087673)
    • (2006) Physics Letters, Section A: General, Atomic and Solid State Physics , vol.350 , Issue.1-2 , pp. 87-88
    • He, J.-H.1
  • 12
    • 71749099144 scopus 로고    scopus 로고
    • N-soliton solutions for a (2+1)-dimensional breaking soliton equation with self-consistent sources
    • 2574918 1186.35179 10.1016/j.na.2009.06.066
    • Y.Q. Yao D.Y. Chen Y.B. Zeng 2010 N-soliton solutions for a (2+1)-dimensional breaking soliton equation with self-consistent sources Nonlinear Anal. 72 57 64 2574918 1186.35179 10.1016/j.na.2009.06.066
    • (2010) Nonlinear Anal. , vol.72 , pp. 57-64
    • Yao, Y.Q.1    Chen, D.Y.2    Zeng, Y.B.3
  • 13
    • 34748839537 scopus 로고    scopus 로고
    • Variational iteration method for solving multispecies Lotka-Volterra equations
    • DOI 10.1016/j.camwa.2006.12.058, PII S0898122107003069, Variational Iteration Method for Nonlinear Problems
    • B. Batiha M.S.M. Noorani I. Hashim 2007 Variational iteration method for solving multispecies Lotka-Volterra equations Comput. Math. Appl. 54 903 909 2395627 1141.65370 10.1016/j.camwa.2006.12.058 (Pubitemid 47488840)
    • (2007) Computers and Mathematics with Applications , vol.54 , Issue.7-8 , pp. 903-909
    • Batiha, B.1    Noorani, M.S.M.2    Hashim, I.3
  • 14
    • 34748831014 scopus 로고    scopus 로고
    • Application of He's methods to nonlinear chemistry problems
    • DOI 10.1016/j.camwa.2006.12.078, PII S0898122107002994, Variational Iteration Method for Nonlinear Problems
    • D.D. Ganji M. Nourollahi E. Mohseni 2007 Application of He's methods to nonlinear chemistry problems Comput. Math. Appl. 54 1122 1132 2398134 05287821 10.1016/j.camwa.2006.12.078 (Pubitemid 47488835)
    • (2007) Computers and Mathematics with Applications , vol.54 , Issue.7-8 , pp. 1122-1132
    • Ganji, D.D.1    Nourollahi, M.2    Mohseni, E.3
  • 15
    • 0036727941 scopus 로고    scopus 로고
    • Exact solutions of some systems of nonlinear partial differential equations using symbolic computation
    • DOI 10.1016/S0898-1221(02)00184-0, PII S0898122102001840
    • F.D. Xie 2002 Exact solutions of some systems of nonlinear partial differential equations using symbolic computation Comput. Math. Appl. 44 711 716 1925814 1030.35025 10.1016/S0898-1221(02)00184-0 (Pubitemid 34974384)
    • (2002) Computers and Mathematics with Applications , vol.44 , Issue.5-6 , pp. 711-716
    • Xie, F.-D.1    Li, M.2    Zhang, Y.3
  • 16
    • 67349144674 scopus 로고    scopus 로고
    • Gevrey regularity for a class of water-wave models
    • 1173.35657 10.1016/j.na.2008.11.047
    • Z. Grujić H. Kalisch 2009 Gevrey regularity for a class of water-wave models Nonlinear Anal. 71 1160 1170 1173.35657 10.1016/j.na.2008.11. 047
    • (2009) Nonlinear Anal. , vol.71 , pp. 1160-1170
    • Grujić, Z.1    Kalisch, H.2
  • 18
    • 0037120098 scopus 로고    scopus 로고
    • Soliton in alpha helical proteins with interspine coupling at higher order
    • 10.1016/S0375-9601(02)01110-6
    • M. Daniel M.M. Lathab 2002 Soliton in alpha helical proteins with interspine coupling at higher order Phys. Lett. A 302 94 104 10.1016/S0375-9601(02)01110-6
    • (2002) Phys. Lett. A , vol.302 , pp. 94-104
    • Daniel, M.1    Lathab, M.M.2
  • 19
    • 0009683072 scopus 로고
    • On the laws of connexion between the conditions of a chemical change and its amount
    • 10.1098/rstl.1866.0010
    • A.V. Harcourt W. Esson 1866 On the laws of connexion between the conditions of a chemical change and its amount Philos. Trans. R. Soc. Lond. 156 193 221 10.1098/rstl.1866.0010
    • (1866) Philos. Trans. R. Soc. Lond. , vol.156 , pp. 193-221
    • Harcourt, A.V.1    Esson, W.2
  • 21
    • 0015484437 scopus 로고
    • Comparing numerical methods for ordinary differential equations
    • 351086 0221.65115 10.1137/0709052
    • T.E. Hull W.H. Enright B.M. Fellen A.E. Sedgwick 1972 Comparing numerical methods for ordinary differential equations SIAM J. Numer. Anal. 9 603 636 351086 0221.65115 10.1137/0709052
    • (1972) SIAM J. Numer. Anal. , vol.9 , pp. 603-636
    • Hull, T.E.1    Enright, W.H.2    Fellen, B.M.3    Sedgwick, A.E.4
  • 22
    • 70350574745 scopus 로고    scopus 로고
    • Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method
    • 2557339 1189.65259 10.1016/j.camwa.2009.03.059
    • N.H. Sweilam M.M. Khader 2009 Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method Comput. Math. Appl. 58 2134 2141 2557339 1189.65259 10.1016/j.camwa.2009.03.059
    • (2009) Comput. Math. Appl. , vol.58 , pp. 2134-2141
    • Sweilam, N.H.1    Khader, M.M.2
  • 23
    • 49149136885 scopus 로고
    • Numerical evaluation of the modified Bessel functions i and K
    • 614177 0456.65006 10.1016/0898-1221(81)90080-8
    • M.A. Gatto J.B. Seery 1981 Numerical evaluation of the modified Bessel functions I and K Comput. Math. Appl. 7 203 209 614177 0456.65006 10.1016/0898-1221(81)90080-8
    • (1981) Comput. Math. Appl. , vol.7 , pp. 203-209
    • Gatto, M.A.1    Seery, J.B.2
  • 24
    • 72949121902 scopus 로고    scopus 로고
    • Jordan type inequalities involving the Bessel and modified Bessel functions
    • 2575562 1189.33010 10.1016/j.camwa.2009.10.020
    • Z. Ling 2010 Jordan type inequalities involving the Bessel and modified Bessel functions Comput. Math. Appl. 59 724 736 2575562 1189.33010 10.1016/j.camwa.2009.10.020
    • (2010) Comput. Math. Appl. , vol.59 , pp. 724-736
    • Ling, Z.1
  • 25
    • 0002566545 scopus 로고    scopus 로고
    • A comparison between Adomian decomposition method and Taylor series method in the series solution
    • 1642543 0943.65084 10.1016/S0096-3003(97)10127-8
    • A.M. Wazwaz 1998 A comparison between Adomian decomposition method and Taylor series method in the series solution Appl. Math. Comput. 97 37 44 1642543 0943.65084 10.1016/S0096-3003(97)10127-8
    • (1998) Appl. Math. Comput. , vol.97 , pp. 37-44
    • Wazwaz, A.M.1
  • 26
    • 79961040282 scopus 로고    scopus 로고
    • Solitonic propagation and interaction for a generalized variable-coefficient forced Korteweg-de Vries equation in fluids
    • 10.1103/PhysRevE.83.056601
    • X. Yu Y.T. Gao Z.Y. Sun Y. Liu 2011 Solitonic propagation and interaction for a generalized variable-coefficient forced Korteweg-de Vries equation in fluids Phys. Rev. E 83 056601 10.1103/PhysRevE.83.056601
    • (2011) Phys. Rev. e , vol.83 , pp. 056601
    • Yu, X.1    Gao, Y.T.2    Sun, Z.Y.3    Liu, Y.4
  • 27
    • 77950984881 scopus 로고    scopus 로고
    • N-soliton solutions, Backlund transformation and Lax pair for a generalized variable-coefficient fifth-order Korteweg-de Vries equation
    • 10.1088/0031-8949/81/04/045402
    • X. Yu Y.T. Gao Z.Y. Sun Y. Liu 2010 N-soliton solutions, Backlund transformation and Lax pair for a generalized variable-coefficient fifth-order Korteweg-de Vries equation Phys. Scr. 81 045402 10.1088/0031-8949/81/04/045402
    • (2010) Phys. Scr. , vol.81 , pp. 045402
    • Yu, X.1    Gao, Y.T.2    Sun, Z.Y.3    Liu, Y.4
  • 28
    • 75349098275 scopus 로고    scopus 로고
    • Bound vector solitons and soliton complexes for the coupled nonlinear Schrödinger equations
    • 10.1103/PhysRevE.80.066608
    • Z.Y. Sun Y.T. Gao X. Yu W.J. Liu Y. Liu 2009 Bound vector solitons and soliton complexes for the coupled nonlinear Schrödinger equations Phys. Rev. E 80 066608 10.1103/PhysRevE.80.066608
    • (2009) Phys. Rev. e , vol.80 , pp. 066608
    • Sun, Z.Y.1    Gao, Y.T.2    Yu, X.3    Liu, W.J.4    Liu, Y.5
  • 29
    • 70350586990 scopus 로고    scopus 로고
    • Inelastic interactions of the multiple-front waves for the modified Kadomtsev-Petviashvili equation in fluid dynamics, plasma physics and electrodynamics
    • 2565175 1231.37045 10.1016/j.wavemoti.2009.06.014
    • Z.Y. Sun Y.T. Gao X. Yu X.H. Meng Y. Liu 2009 Inelastic interactions of the multiple-front waves for the modified Kadomtsev-Petviashvili equation in fluid dynamics, plasma physics and electrodynamics Wave Motion 46 511 2565175 1231.37045 10.1016/j.wavemoti.2009.06.014
    • (2009) Wave Motion , vol.46 , pp. 511
    • Sun, Z.Y.1    Gao, Y.T.2    Yu, X.3    Meng, X.H.4    Liu, Y.5
  • 30
    • 78149381952 scopus 로고    scopus 로고
    • Inelastic interactions and double Wronskian solutions for the Whitham-Broer-Kaup model in shallow water
    • 10.1088/0031-8949/80/06/065017
    • L. Wang Y.T. Gao X.L. Gai Z.Y. Sun 2009 Inelastic interactions and double Wronskian solutions for the Whitham-Broer-Kaup model in shallow water Phys. Scr. 80 065017 10.1088/0031-8949/80/06/065017
    • (2009) Phys. Scr. , vol.80 , pp. 065017
    • Wang, L.1    Gao, Y.T.2    Gai, X.L.3    Sun, Z.Y.4
  • 31
    • 77958157287 scopus 로고    scopus 로고
    • Odd-soliton-like solutions for the variable-coefficient variant Boussinesq model in the long gravity waves
    • 1205.05083
    • L. Wang Y.T. Gao X.L. Gai 2010 Odd-soliton-like solutions for the variable-coefficient variant Boussinesq model in the long gravity waves Z. Naturforsch. A 65 1 1205.05083
    • (2010) Z. Naturforsch. A , vol.65 , pp. 1
    • Wang, L.1    Gao, Y.T.2    Gai, X.L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.