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Volumn 11, Issue 2, 2010, Pages 637-644

Method for solving nonlinear initial value problems by combining homotopy perturbation and reproducing kernel Hilbert space methods

Author keywords

Homotopy perturbation method; Lane Emden type equations; Nonlinear; Reproducing kernel Hilbert space method; Singular initial value problem

Indexed keywords

ANALYTICAL TECHNIQUES; CONVERGENT SERIES; HOMOTOPIES; HOMOTOPY PERTURBATION METHOD; LANE-EMDEN-TYPE EQUATIONS; LINEAR PROBLEMS; NON-HOMOGENEOUS; NONLINEAR INITIAL-VALUE PROBLEMS; NONLINEAR PROBLEMS; NUMERICAL EXAMPLE; PERTURBATION METHOD; REPRODUCING KERNEL HILBERT SPACES; RIGHT-HAND SIDES; SINGULAR POINTS;

EID: 70449630210     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2008.10.033     Document Type: Article
Times cited : (38)

References (51)
  • 4
    • 0037799370 scopus 로고    scopus 로고
    • Linearization method in classical and quantum mechanics
    • Ramos J.I. Linearization method in classical and quantum mechanics. Computer Physics Communications 153 (2003) 199-208
    • (2003) Computer Physics Communications , vol.153 , pp. 199-208
    • Ramos, J.I.1
  • 5
    • 10044270006 scopus 로고    scopus 로고
    • Linearization techniques for singular initial-value problems of ordinary differential equations
    • Ramos J.I. Linearization techniques for singular initial-value problems of ordinary differential equations. Appl. Math. Comput. 161 (2005) 525-542
    • (2005) Appl. Math. Comput. , vol.161 , pp. 525-542
    • Ramos, J.I.1
  • 6
    • 0040926145 scopus 로고    scopus 로고
    • A new algorithm for solving differential equations of Lane-Emden type
    • Wazwaz A.M. A new algorithm for solving differential equations of Lane-Emden type. Appl. Math. Comput. 118 (2001) 287-310
    • (2001) Appl. Math. Comput. , vol.118 , pp. 287-310
    • Wazwaz, A.M.1
  • 7
    • 0037052586 scopus 로고    scopus 로고
    • A new method for solving singular initial value problems in second-order ordinary differential equations
    • Wazwaz A.M. A new method for solving singular initial value problems in second-order ordinary differential equations. Applied Mathematics and Computation 128 (2002) 45-57
    • (2002) Applied Mathematics and Computation , vol.128 , pp. 45-57
    • Wazwaz, A.M.1
  • 8
    • 32144452761 scopus 로고    scopus 로고
    • The modified decomposition method for analytic treatment of differential equations
    • Wazwaz A.M. The modified decomposition method for analytic treatment of differential equations. Applied Mathematics Computation 173 (2006) 165-176
    • (2006) Applied Mathematics Computation , vol.173 , pp. 165-176
    • Wazwaz, A.M.1
  • 9
    • 34548249064 scopus 로고    scopus 로고
    • Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method
    • Yi{dotless}ldi{dotless}ri{dotless}m A., and Öziş T. Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method. Physics Letters A 369 (2007) 70-76
    • (2007) Physics Letters A , vol.369 , pp. 70-76
    • Yildirim, A.1    Öziş, T.2
  • 10
    • 59049085436 scopus 로고    scopus 로고
    • Solutions of singular IVPs of Lane-Emden type by the variational iteration method
    • 10.1016/j.na.2008.03.012
    • Yi{dotless}ldi{dotless}ri{dotless}m A., and Öziş T. Solutions of singular IVPs of Lane-Emden type by the variational iteration method. Nonlinear Analysis (2008) 10.1016/j.na.2008.03.012
    • (2008) Nonlinear Analysis
    • Yildirim, A.1    Öziş, T.2
  • 11
    • 47749116910 scopus 로고    scopus 로고
    • Further developments to the decomposition method for solving singular initial value problems
    • Aslanov A., and Abu-Alshaikh I. Further developments to the decomposition method for solving singular initial value problems. Mathematical and Computer Modelling 48 5-6 (2008) 700-711
    • (2008) Mathematical and Computer Modelling , vol.48 , Issue.5-6 , pp. 700-711
    • Aslanov, A.1    Abu-Alshaikh, I.2
  • 12
    • 0034580670 scopus 로고    scopus 로고
    • Iterated defect correction for the solution of singular initial value problems
    • Koch O., and Weinmuller E.B. Iterated defect correction for the solution of singular initial value problems. SIAM Journal on Numerical Analysis 38 6 (2001) 1784-1799
    • (2001) SIAM Journal on Numerical Analysis , vol.38 , Issue.6 , pp. 1784-1799
    • Koch, O.1    Weinmuller, E.B.2
  • 14
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of a homotopy technique and a perturbation technique for non-linear problems
    • He J.H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. International Journal of Nonlinear Mechanics 35 1 (2000) 37-43
    • (2000) International Journal of Nonlinear Mechanics , vol.35 , Issue.1 , pp. 37-43
    • He, J.H.1
  • 15
    • 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 1 (2003) 73-79
    • (2003) Applied Mathematics and Computation , vol.135 , Issue.1 , pp. 73-79
    • He, J.H.1
  • 16
    • 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 1 (2004) 287-292
    • (2004) Applied Mathematics and Computation , vol.151 , Issue.1 , pp. 287-292
    • He, J.H.1
  • 17
    • 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 2 (2004) 527-539
    • (2004) Applied Mathematics and Computation , vol.156 , Issue.2 , pp. 527-539
    • He, J.H.1
  • 19
    • 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 3 (2005) 695-700
    • (2005) Chaos, Solitons and Fractals , vol.26 , Issue.3 , pp. 695-700
    • He, J.H.1
  • 20
    • 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 1-2 (2006) 87-88
    • (2006) Physics Letters A , vol.350 , Issue.1-2 , pp. 87-88
    • He, J.H.1
  • 21
    • 33748922411 scopus 로고    scopus 로고
    • Non-perturbative methods for strongly nonlinear problems
    • Dissertation, de-Verlag in GmbH, Berlin
    • J.H. He, Non-perturbative methods for strongly nonlinear problems, Dissertation, de-Verlag in GmbH, Berlin, 2006
    • (2006)
    • He, J.H.1
  • 22
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equation
    • He J.H. Some asymptotic methods for strongly nonlinear equation. International Journal of Modern Physics B 20 10 (2006) 1141-1199
    • (2006) International Journal of Modern Physics B , vol.20 , Issue.10 , pp. 1141-1199
    • He, J.H.1
  • 23
    • 33746584753 scopus 로고    scopus 로고
    • Addendum new interpretation of homotopy perturbation method
    • He J.H. Addendum new interpretation of homotopy perturbation method. International Journal of Modern Physics B 20 18 (2006) 2561-2568
    • (2006) International Journal of Modern Physics B , vol.20 , Issue.18 , pp. 2561-2568
    • He, J.H.1
  • 25
    • 34548580632 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving a nonlinear system of second order boundary value problems
    • Yusufoǧlu E. Homotopy perturbation method for solving a nonlinear system of second order boundary value problems. International Journal of Nonlinear Sciences and Numerical Simulation 8 3 (2007) 353-358
    • (2007) International Journal of Nonlinear Sciences and Numerical Simulation , vol.8 , Issue.3 , pp. 353-358
    • Yusufoǧlu, E.1
  • 27
    • 35748957246 scopus 로고    scopus 로고
    • Application of He's homotopy perturbation method to the relativistic (An)harmonic oscillator. I: Comparison between approximate and exact frequencies
    • Beléndez A., Pascual C., Márquez A., and Méndez D.I. Application of He's homotopy perturbation method to the relativistic (An)harmonic oscillator. I: Comparison between approximate and exact frequencies. International Journal of Nonlinear Sciences and Numerical Simulation 8 4 (2007) 483-492
    • (2007) International Journal of Nonlinear Sciences and Numerical Simulation , vol.8 , Issue.4 , pp. 483-492
    • Beléndez, A.1    Pascual, C.2    Márquez, A.3    Méndez, D.I.4
  • 29
    • 35348938590 scopus 로고    scopus 로고
    • Solving fractional diffusion and wave equations by modified homotopy perturbation method
    • Jafari H., and Momani S. Solving fractional diffusion and wave equations by modified homotopy perturbation method. Physics Letters A 370 5-6 (2007) 388-396
    • (2007) Physics Letters A , vol.370 , Issue.5-6 , pp. 388-396
    • Jafari, H.1    Momani, S.2
  • 30
    • 50349083334 scopus 로고    scopus 로고
    • Application of a modified He's homotopy perturbation method to obtain higher-order approximations to a nonlinear oscillator with discontinuities
    • Beléndez A., Pascual C., Beléndez T., and Hernndez A. Application of a modified He's homotopy perturbation method to obtain higher-order approximations to a nonlinear oscillator with discontinuities. Nonlinear Analysis: Real World Applications 10 1 (2009) 416-427
    • (2009) Nonlinear Analysis: Real World Applications , vol.10 , Issue.1 , pp. 416-427
    • Beléndez, A.1    Pascual, C.2    Beléndez, T.3    Hernndez, A.4
  • 31
    • 34748873765 scopus 로고    scopus 로고
    • The three-dimensional flow past a stretching sheet and the homotopy perturbation method
    • Ariel P.D. The three-dimensional flow past a stretching sheet and the homotopy perturbation method. Computers, Mathematics with Applications 54 7-8 (2007) 1018-1027
    • (2007) Computers, Mathematics with Applications , vol.54 , Issue.7-8 , pp. 1018-1027
    • Ariel, P.D.1
  • 32
    • 34748871953 scopus 로고    scopus 로고
    • He's homotopy perturbation method for a boundary layer equation in unbounded domain
    • Xu L. He's homotopy perturbation method for a boundary layer equation in unbounded domain. Computers, Mathematics with Applications 54 7-8 (2007) 1067-1070
    • (2007) Computers, Mathematics with Applications , vol.54 , Issue.7-8 , pp. 1067-1070
    • Xu, L.1
  • 33
    • 34250636701 scopus 로고    scopus 로고
    • Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations
    • Ganji D.D., and Sadighi A. Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations. Journal of Computational and Applied Mathematics 207 1 (2007) 24-34
    • (2007) Journal of Computational and Applied Mathematics , vol.207 , Issue.1 , pp. 24-34
    • Ganji, D.D.1    Sadighi, A.2
  • 34
    • 34250740001 scopus 로고    scopus 로고
    • Application of He's homotopy perturbation method for nth-order integro-differential equations
    • Golbabai A., and Javidi M. Application of He's homotopy perturbation method for nth-order integro-differential equations. Applied Mathematics and Computation 190 2 (2007) 1409-1416
    • (2007) Applied Mathematics and Computation , vol.190 , Issue.2 , pp. 1409-1416
    • Golbabai, A.1    Javidi, M.2
  • 35
    • 34250643564 scopus 로고    scopus 로고
    • Homotopy perturbation method for fractional KdV equation
    • Wang Q. Homotopy perturbation method for fractional KdV equation. Applied Mathematics and Computation 190 2 (2007) 1795-1802
    • (2007) Applied Mathematics and Computation , vol.190 , Issue.2 , pp. 1795-1802
    • Wang, Q.1
  • 36
    • 34248375297 scopus 로고    scopus 로고
    • A new modification of the homotopy perturbation method for linear and nonlinear operators
    • Odibat Z.M. A new modification of the homotopy perturbation method for linear and nonlinear operators. Applied Mathematics and Computation 189 1 (2007) 341-345
    • (2007) Applied Mathematics and Computation , vol.189 , Issue.1 , pp. 341-345
    • Odibat, Z.M.1
  • 37
    • 34548154022 scopus 로고    scopus 로고
    • Application of homotopy perturbation method for solving eighth-order boundary value problems
    • Golbabai A., and Javidi M. Application of homotopy perturbation method for solving eighth-order boundary value problems. Applied Mathematics and Computation 191 (2007) 334-346
    • (2007) Applied Mathematics and Computation , vol.191 , pp. 334-346
    • Golbabai, A.1    Javidi, M.2
  • 40
    • 34548817286 scopus 로고    scopus 로고
    • Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space
    • Geng F., and Cui M. Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space. Applied Mathematics and Computation 192 (2007) 389-398
    • (2007) Applied Mathematics and Computation , vol.192 , pp. 389-398
    • Geng, F.1    Cui, M.2
  • 41
    • 33750972868 scopus 로고    scopus 로고
    • Solving a nonlinear system of second order boundary value problems
    • Geng F., and Cui M. Solving a nonlinear system of second order boundary value problems. Journal of Mathematical Analysis and Applications 327 (2007) 1167-1181
    • (2007) Journal of Mathematical Analysis and Applications , vol.327 , pp. 1167-1181
    • Geng, F.1    Cui, M.2
  • 42
    • 43649091637 scopus 로고    scopus 로고
    • Solving singular nonlinear two-point boundary value problems in the reproducing kernel space
    • Geng F., and Cui M. Solving singular nonlinear two-point boundary value problems in the reproducing kernel space. Journal of the Korean Mathematical Society 45 3 (2008) 631-644
    • (2008) Journal of the Korean Mathematical Society , vol.45 , Issue.3 , pp. 631-644
    • Geng, F.1    Cui, M.2
  • 43
    • 34247369424 scopus 로고    scopus 로고
    • Solving singular two-point boundary value problem in reproducing kernel space
    • Cui M., and Geng F. Solving singular two-point boundary value problem in reproducing kernel space. Journal of Computational and Applied Mathematics 205 (2007) 6-15
    • (2007) Journal of Computational and Applied Mathematics , vol.205 , pp. 6-15
    • Cui, M.1    Geng, F.2
  • 44
    • 40849132839 scopus 로고    scopus 로고
    • A computational method for solving third-order singularly perturbed boundary-value problems
    • Cui M., and Geng F. A computational method for solving third-order singularly perturbed boundary-value problems. Applied Mathematics and Computation 198 (2008) 896-903
    • (2008) Applied Mathematics and Computation , vol.198 , pp. 896-903
    • Cui, M.1    Geng, F.2
  • 45
    • 34248231712 scopus 로고    scopus 로고
    • A computational method for solving one-dimensional variable-coefficient Burgers equation
    • Cui M., and Geng F. A computational method for solving one-dimensional variable-coefficient Burgers equation. Applied Mathematics and Computation 188 (2007) 1389-1401
    • (2007) Applied Mathematics and Computation , vol.188 , pp. 1389-1401
    • Cui, M.1    Geng, F.2
  • 46
    • 34547300818 scopus 로고    scopus 로고
    • A new method of solving the coefficient inverse problem of differential equation
    • Cui M., and Lin Y. A new method of solving the coefficient inverse problem of differential equation. Science in China Series A 50 4 (2007) 561-572
    • (2007) Science in China Series A , vol.50 , Issue.4 , pp. 561-572
    • Cui, M.1    Lin, Y.2
  • 47
    • 25644441574 scopus 로고    scopus 로고
    • Representation of the exact solution for infinite system of linear equations
    • Yingzhen L., Minggen C., and Yi Z. Representation of the exact solution for infinite system of linear equations. Applied Mathematics and Computation 168 (2005) 636-650
    • (2005) Applied Mathematics and Computation , vol.168 , pp. 636-650
    • Yingzhen, L.1    Minggen, C.2    Yi, Z.3
  • 48
    • 33646467101 scopus 로고    scopus 로고
    • Representation of the exact solution for a kind of nonlinear partial differential equations
    • Lin Y., Cui M., and Yang L. Representation of the exact solution for a kind of nonlinear partial differential equations. Applied Mathematics Letters 19 (2006) 808-813
    • (2006) Applied Mathematics Letters , vol.19 , pp. 808-813
    • Lin, Y.1    Cui, M.2    Yang, L.3
  • 49
    • 34047244924 scopus 로고    scopus 로고
    • The exact solution of nonlinear age-structured population model
    • Cui M., and Chen Z. The exact solution of nonlinear age-structured population model. Nonlinear Analysis: Real World Applications 8 (2007) 1096-1112
    • (2007) Nonlinear Analysis: Real World Applications , vol.8 , pp. 1096-1112
    • Cui, M.1    Chen, Z.2
  • 50
    • 0037845043 scopus 로고    scopus 로고
    • The exact solution for solving a class nonlinear operator equations in the reproducing kernel space
    • Li C., and Cui M. The exact solution for solving a class nonlinear operator equations in the reproducing kernel space. Applied Mathematics and Computation 143 (2003) 393-399
    • (2003) Applied Mathematics and Computation , vol.143 , pp. 393-399
    • Li, C.1    Cui, M.2
  • 51
    • 0037114105 scopus 로고    scopus 로고
    • How to solve the equation AuBu + Cu = f
    • Li C., and Cui M. How to solve the equation AuBu + Cu = f. Applied Mathematics and Computation 133 (2002) 643-653
    • (2002) Applied Mathematics and Computation , vol.133 , pp. 643-653
    • Li, C.1    Cui, M.2


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