Analytical solution for the FokkerPlanck equation by differential transform method

Scientia Iranica

Volumn 19, Issue 4, 2012, Pages 1140-1145

  Hesam, S ^a   Nazemi, A R ^a   Haghbin, A ^b  

^a SHAHROOD UNIVERSITY OF TECHNOLOGY   (Iran)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Brownian motion; Closed form solution; Differential transform method; Fokker planck equation; Kolmogorov equation

Indexed keywords

BROWNIAN MOVEMENT; COMPUTATIONAL COMPLEXITY; FLOW MEASUREMENT;

CLOSED FORM SOLUTIONS; COMPUTATIONAL WORK; DIFFERENTIAL TRANSFORM METHOD; KOLMOGOROV EQUATIONS; NONLINEAR PROBLEMS; RAPIDLY CONVERGENT SERIES; SIMPLE SCHEMES;

FOKKER PLANCK EQUATION;

ANALYTICAL FRAMEWORK; BROWNIAN MOTION; COMPUTER SIMULATION; LINEARITY; NONLINEARITY; TRANSFORM;

EID: 84865205943     PISSN: 10263098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.scient.2012.06.018     Document Type: Article

References (45)

1. H. Risken The FokkerPlanck Equation Method of Solution and Applications 1989 Springer Verlag Berlin, Heidelberg
2. T.D. Frank Stochastic feedback, nonlinear families of Markov processes, and nonlinear FokkerPlanck equations Phys. Lett. A 331 2004 391 408
3. C. Buet, S. Dellacherie, and R. Sentis Numerical solution of a ionic FokkerPlanck equation with electronic temperature SIAM J. Numer. Anal. 39 2001 1219 1253
4. G. Harrison Numerical solution of the FokkerPlanck equation using moving finite elements Numer. Methods Partial Differential Equations 4 1988 219 232
5. S. Hesam, A.R. Nazemi, and A. Haghbin Analytical solution for the ZakharovKuznetsov equations by differential transform method Internat. J. Engrg. Sci. 4 2010 235 240
6. S. Hesam, A.R. Nazemi, and A. Haghbin Reduced differential transform method for solving the FornbergWhitham type equation Int. J. Nonlinear Sci. 13 2 2012 158 162
7. M. Lakestani, and M. Dehghan Numerical solution of FokkerPlanck equation using the cubic B-spline scaling functions Numer. Methods Partial Differential Equations 25 2009 418 429
8. V. Palleschi, F. Sarri, G. Marcozzi, and M.R. Torquati Numerical solution of the FokkerPlanck equation: a fast and accurate algorithm Phys. Lett. A 146 1990 378 386
9. V. Palleschi, and M. de Rosa Numerical solution of the FokkerPlanck equation. II. Multidimensional case Phys. Lett. A 163 1992 381 391
10. A. Sadighi, D.D. Ganji, and Y. Sabzehmeidani A study on FokkerPlanck equation by variational iteration and homotopy-perturbation methods Int. J. Nonlinear Sci. 4 2007 92 102
11. M. Tatari, M. Dehghan, and M. Razzaghi Application of the Adomian decomposition method for the FokkerPlanck equation Math. Comput. Modelling 45 2007 639 650 (Pubitemid 44829928)
12. V. Vanaja Numerical solution of simple FokkerPlanck equation Appl. Numer. Math. 9 1992 533 540
13. M.P. Zorzano, H. Mais, and L. Vazquez Numerical solution of two-dimensional FokkerPlanck equations Appl. Math. Comput. 98 1999 109 117
14. J.K. Zhou Differential Transformation and Its Applications for Electrical Circuits 1986 Huazhong University Press Wuhan, China (in Chinese)
15. A.K. Alomari A new analytic solution for fractional chaotic dynamical systems using the differential transform method Comput. Math. Appl. 61 2011 2528 2534
16. A.V. Al-rabtah, S. Ertrk, and S. Momania Solutions of a fractional oscillator by using differential transform method Comput. Math. Appl. 59 2010 1356 1362
17. A. Arikoglu, and I. Ozkol Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method Compos. Struct. 92 2010 3031 3039
18. J. Biazar, and M. Eslami Analytic solution for Telegraph equation by differential transform method Phys. Lett. A 374 2010 2904 2906
19. etinkaya, A. and Kiymaz, O. "The solution of the time-fractional diffusion equation by the generalized differential transform method", Math. Comput. Modelling (in press).
20. O. Demirdag, and Y. Yesilce Solution of free vibration equation of elastically supported Timoshenko columns with a tip mass by differential transform method Adv. Eng. Softw. 42 2011 860 867
21. A. Elsaid Fractional differential transform method combined with the Adomian polynomials Appl. Math. Comput. 218 2012 6899 6911
22. M. El-Shahed Application of differential transform method to non-linear oscillatory systems Commun. Nonlinear Sci. Numer. Simul. 13 2008 1714 1720 (Pubitemid 351258882)
23. H. Fatoorehchi, and H. Abolghasemi Computation of analytical Laplace transforms by the differential transform method Math. Comput. Modelling 56 2012 145 151
24. A. Gkdoan, M. Merdan, and A. Yildirim The modified algorithm for the differential transform method to solution of Genesio systems Commun. Nonlinear Sci. Numer. Simul. 17 2012 45 51
25. P.K. Gupta Approximate analytical solutions of fractional BenneyLin equation by reduced differential transform method and the homotopy perturbation method Comput. Math. Appl. 61 2011 2829 2842
26. B. Jang Solving linear and nonlinear initial value problems by the projected differential transform method Comput. Phys. Commun. 181 2010 848 854
27. M. Keimanesh, M.M. Rashidi, A.J. Chamkha, and R. Jafari Study of a third grade non-Newtonian fluid flow between two parallel plates using the multi-step differential transform method Comput. Math. Appl. 62 2011 2871 2891
28. M. Kurulay, and M. Bayram Approximate analytical solution for the fractional modified KdV by differential transform method Commun. Nonlinear Sci. Numer. Simul. 15 2010 1777 1782
29. J. Liu, and G. Hou Numerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform method Appl. Math. Comput. 217 2011 7001 7008
30. S. Momani, and V.S. Ertrk Solutions of non-linear oscillators by the modified differential transform method Comput. Math. Appl. 55 2008 833 842
31. D. Nazari, and S. Shahmorad Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions J. Comput. Appl. Math. 234 2010 883 891
32. Z. Odibat, C. Bertelle, M.A. Aziz-Alaoui, and G.H.E. Duchampd A multi-step differential transform method and application to non-chaotic or chaotic systems Comput. Math. Appl. 59 2010 1462 1472
33. A.S.V. Ravi Kanth, and K. Aruna Two-dimensional differential transform method for solving linear and non-linear Schrdinger equations Chaos Solitons Fractals 41 2009 2277 2281
34. A.S.V. Ravi Kanth, and K. Aruna Differential transform method for solving the linear and nonlinear KleinGordon equation Comput. Phys. Commun. 180 2009 708 711
35. A.S.V. Ravi Kanth, and K. Aruna Differential transform method for solving linear and non-linear systems of partial differential equations Phys. Lett. A 372 2008 6896 6898
36. A. Tari, M.Y. Rahimi, S. Shahmorad, and F. Talati Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method J. Comput. Appl. Math. 228 2009 70 76
37. A. Tari, and S. Shahmorad Differential transform method for the system of two-dimensional nonlinear Volterra integro-differential equations Comput. Math. Appl. 61 2011 2621 2629
38. M. Thongmoon, and S. Pusjuso The numerical solutions of differential transform method and the Laplace transform method for a system of differential equations Nonlinear Anal. Hybrid Syst. 4 2010 425 431
39. Erdnmez, and I. zkol Optimal shape analysis of a column structure under various loading conditions by using differential transform method (DTM) Appl. Math. Comput. 216 2010 3172 3183
40. X. Yang, Y. Liu, and S. Bai A numerical solution of second-order linear partial differential equations by differential transform Appl. Math. Comput. 173 2006 792 802 (Pubitemid 43243538)
41. L. Zou, Z. Zong, Z. Wangd, and S. Tian Differential transform method for solving solitary wave with discontinuity Phys. Lett. A 374 2010 3451 3454
42. M.-J. Jang, C.-L. Chen, and Y.-C. Liu Two-dimensional differential transform for partial differential equations Appl. Math. Comput. 121 2001 261 270 (Pubitemid 32427582)
43. F. Ayaz On the two-dimensional differential transform method Appl. Math. Comput. 143 2003 361 374
44. C.K. Chen, and S.H. Ho Solving partial differential equations by two dimensional differential transform Appl. Math. Comput. 106 1999 171 179
45. F. Ayaz Solutions of the system of differential equations by differential transform method Appl. Math. Comput. 147 2004 547 567