메뉴 건너뛰기




Volumn 15, Issue 7, 2010, Pages 1921-1927

Approximate periodic solutions for the non-linear relativistic harmonic oscillator via differential transformation method

Author keywords

Aftertreatment technique; Differential transformation method; Periodic solutions; Relativistic harmonic oscillator

Indexed keywords

LINEAR TRANSFORMATIONS; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; OSCILLATORS (MECHANICAL);

EID: 74849097716     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.07.003     Document Type: Article
Times cited : (41)

References (26)
  • 1
    • 85010249266 scopus 로고
    • The relativistic linear harmonic oscillator
    • Penfield R., and Zatzkis H. The relativistic linear harmonic oscillator. J Franklin Inst 262 (1956) 121
    • (1956) J Franklin Inst , vol.262 , pp. 121
    • Penfield, R.1    Zatzkis, H.2
  • 2
    • 49749186703 scopus 로고
    • Note on the relativistic harmonic oscillator
    • Gold L. Note on the relativistic harmonic oscillator. J Franklin Inst (1957) 25-27
    • (1957) J Franklin Inst , pp. 25-27
    • Gold, L.1
  • 3
    • 0001558206 scopus 로고    scopus 로고
    • Periodic solutions of the relativistic harmonic oscillator
    • Mickens R.E. Periodic solutions of the relativistic harmonic oscillator. J Sound Vib 212 (1998) 905-908
    • (1998) J Sound Vib , vol.212 , pp. 905-908
    • Mickens, R.E.1
  • 6
    • 0032040849 scopus 로고    scopus 로고
    • Analysis of general elastically end restrained non-uniform beams using differential transform
    • Ho S.H., and Chen C.K. Analysis of general elastically end restrained non-uniform beams using differential transform. Appl Math Model 22 (1998) 219-234
    • (1998) Appl Math Model , vol.22 , pp. 219-234
    • Ho, S.H.1    Chen, C.K.2
  • 7
    • 0344286739 scopus 로고    scopus 로고
    • Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform
    • Chen C.K., and Ho S.H. Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform. Int J Mech Sci 41 (1999) 1339-1356
    • (1999) Int J Mech Sci , vol.41 , pp. 1339-1356
    • Chen, C.K.1    Ho, S.H.2
  • 8
    • 0000443213 scopus 로고    scopus 로고
    • On solving the initial-value problems using the differential transformation method
    • Jang M.-J., Chen C.-L., and Liy Y.-C. On solving the initial-value problems using the differential transformation method. Appl Math Comput 115 (2000) 145-160
    • (2000) Appl Math Comput , vol.115 , pp. 145-160
    • Jang, M.-J.1    Chen, C.-L.2    Liy, Y.-C.3
  • 9
    • 0036832913 scopus 로고    scopus 로고
    • Analysis of nonlinear circuits by using differential Taylor transform
    • Köksal M., and Herdem S. Analysis of nonlinear circuits by using differential Taylor transform. Comput Electr Eng 28 (2002) 513-525
    • (2002) Comput Electr Eng , vol.28 , pp. 513-525
    • Köksal, M.1    Herdem, S.2
  • 10
    • 0037054950 scopus 로고    scopus 로고
    • Different applications for the differential transformation in the differential equations
    • Abdel-Halim Hassan I.H. Different applications for the differential transformation in the differential equations. Appl Math Comput 129 (2002) 183-201
    • (2002) Appl Math Comput , vol.129 , pp. 183-201
    • Abdel-Halim Hassan, I.H.1
  • 11
    • 26044470185 scopus 로고    scopus 로고
    • Solution of boundary value problems for integro-differential equations by using differential transform method
    • Arikoglu A., and Ozkol I. Solution of boundary value problems for integro-differential equations by using differential transform method. Appl Math Comput 168 (2005) 1145-1158
    • (2005) Appl Math Comput , vol.168 , pp. 1145-1158
    • Arikoglu, A.1    Ozkol, I.2
  • 12
    • 44449088392 scopus 로고    scopus 로고
    • Solution of singular two-point boundary value problems using differential transformation method
    • Ravi Kanth A.S.V., and Aruna K. Solution of singular two-point boundary value problems using differential transformation method. Phys Lett A 372 (2008) 4671-4673
    • (2008) Phys Lett A , vol.372 , pp. 4671-4673
    • Ravi Kanth, A.S.V.1    Aruna, K.2
  • 13
    • 0006035689 scopus 로고    scopus 로고
    • Solving partial differential equations by two-dimensional differential transform method
    • Chen C.K., and Ho S.H. Solving partial differential equations by two-dimensional differential transform method. Appl Math Comput 41 (1999) 171-179
    • (1999) Appl Math Comput , vol.41 , pp. 171-179
    • Chen, C.K.1    Ho, S.H.2
  • 14
    • 0035877251 scopus 로고    scopus 로고
    • Two-dimensional differential transform for partial differential equations
    • Jang M.-J., Chen C.-L., and Liy Y.-C. Two-dimensional differential transform for partial differential equations. Appl Math Comput 121 (2001) 261-270
    • (2001) Appl Math Comput , vol.121 , pp. 261-270
    • Jang, M.-J.1    Chen, C.-L.2    Liy, Y.-C.3
  • 15
    • 0037507436 scopus 로고    scopus 로고
    • On two-dimensional differential transform method
    • Ayaz F. On two-dimensional differential transform method. Appl Math Comput 143 (2003) 361-374
    • (2003) Appl Math Comput , vol.143 , pp. 361-374
    • Ayaz, F.1
  • 16
    • 0141961581 scopus 로고    scopus 로고
    • Solutions of the system of differential equations by differential transform method
    • Ayaz F. Solutions of the system of differential equations by differential transform method. Appl Math Comput 147 (2004) 547-567
    • (2004) Appl Math Comput , vol.147 , pp. 547-567
    • Ayaz, F.1
  • 17
    • 37349013500 scopus 로고    scopus 로고
    • A new algorithm for calculating one-dimensional differential transform of nonlinear functions
    • Chang S.-H., and Chang I.-L. A new algorithm for calculating one-dimensional differential transform of nonlinear functions. Appl Math Comput 195 (2008) 799-808
    • (2008) Appl Math Comput , vol.195 , pp. 799-808
    • Chang, S.-H.1    Chang, I.-L.2
  • 18
    • 0036499003 scopus 로고    scopus 로고
    • An aftertreatment technique for improving the accuracy of Adomian's decomposition method
    • Jiao Y.C., Yamamoto Y., Dang C., and Hao Y. An aftertreatment technique for improving the accuracy of Adomian's decomposition method. Comput Math Appl 43 (2002) 783-798
    • (2002) Comput Math Appl , vol.43 , pp. 783-798
    • Jiao, Y.C.1    Yamamoto, Y.2    Dang, C.3    Hao, Y.4
  • 19
    • 39349113349 scopus 로고    scopus 로고
    • Application of differential transform method to non-linear oscillatory systems
    • El-Shahed M. Application of differential transform method to non-linear oscillatory systems. Commun Nonlinear Sci Numer Simul 13 (2008) 1714-1720
    • (2008) Commun Nonlinear Sci Numer Simul , vol.13 , pp. 1714-1720
    • El-Shahed, M.1
  • 20
    • 37649020448 scopus 로고    scopus 로고
    • Solutions of non-linear oscillators by the modified differential transform method
    • Momani S., and Ertürk V.S. Solutions of non-linear oscillators by the modified differential transform method. Comput Math Appl 55 (2008) 833-842
    • (2008) Comput Math Appl , vol.55 , pp. 833-842
    • Momani, S.1    Ertürk, V.S.2
  • 21
    • 67649333430 scopus 로고    scopus 로고
    • Two-dimensional differential transform method for solving linear and non-linear Schrdinger equations
    • doi:10.1016/j.chaos.2008.08.037
    • Ravi Kanth ASV, Aruna K. Two-dimensional differential transform method for solving linear and non-linear Schrdinger equations. Chaos Solitons Fract. doi:10.1016/j.chaos.2008.08.037.
    • Chaos Solitons Fract
    • Ravi Kanth, A.S.V.1    Aruna, K.2
  • 22
    • 61849114184 scopus 로고    scopus 로고
    • Differential transform method for solving the linear and nonlinear Klein-Gordon equation
    • Ravi Kanth A.S.V., and Aruna K. Differential transform method for solving the linear and nonlinear Klein-Gordon equation. Comput Phys Commun 180 (2009) 708-711
    • (2009) Comput Phys Commun , vol.180 , pp. 708-711
    • Ravi Kanth, A.S.V.1    Aruna, K.2
  • 23
    • 55549140509 scopus 로고    scopus 로고
    • Application of the differential transformation method for the solution of the hyperchaotic Rössler system
    • Mossa Al-Sawalha M., and Noorani M.S.M. Application of the differential transformation method for the solution of the hyperchaotic Rössler system. Commun Nonlinear Sci Numer Simul 14 (2009) 1509-1514
    • (2009) Commun Nonlinear Sci Numer Simul , vol.14 , pp. 1509-1514
    • Mossa Al-Sawalha, M.1    Noorani, M.S.M.2
  • 24
    • 57049179679 scopus 로고    scopus 로고
    • Application of the differential transformation method to the solution of a damped system with high nonlinearity
    • Kuo B.-L., and Lo C.-Y. Application of the differential transformation method to the solution of a damped system with high nonlinearity. Nonlinear Anal 70 (2009) 1732-1737
    • (2009) Nonlinear Anal , vol.70 , pp. 1732-1737
    • Kuo, B.-L.1    Lo, C.-Y.2
  • 25
    • 43049113844 scopus 로고    scopus 로고
    • Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam
    • Mei C. Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam. Comput Struct 86 (2008) 1280-1284
    • (2008) Comput Struct , vol.86 , pp. 1280-1284
    • Mei, C.1
  • 26
    • 39149142200 scopus 로고    scopus 로고
    • Hybrid differential transform and finite difference method to solve the nonlinear heat conduction problem
    • Chu H.-P., and Chen C.-L. Hybrid differential transform and finite difference method to solve the nonlinear heat conduction problem. Commun Nonlinear Sci Numer Simul 13 (2008) 1605-1614
    • (2008) Commun Nonlinear Sci Numer Simul , vol.13 , pp. 1605-1614
    • Chu, H.-P.1    Chen, C.-L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.