A new piecewise-spectral homotopy analysis method for solving chaotic systems of initial value problems

Mathematical Problems in Engineering

Volumn 2013, Issue , 2013, Pages

  Saberi Nik, H ^a   Effati, Sohrab ^a   Motsa, Sandile S ^b   Shateyi, Stanford ^c  

^a FERDOWSI UNIVERSITY OF MASHHAD   (Iran)

^b UNIVERSITY OF KWAZULU NATAL   (South Africa)

^c UNIVERSITY OF VENDA   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM FOR SOLVING; CHEBYSHEV COLLOCATION; DIFFERENTIAL EQUATION SYSTEMS; GENESIO-TESI SYSTEMS; HOMOTOPY ANALYSIS METHODS; LEGENDRE COLLOCATIONS; NEW APPLICATIONS; SPECTRAL HOMOTOPY ANALYSIS METHODS;

CHAOTIC SYSTEMS; DIFFERENTIAL EQUATIONS;

INITIAL VALUE PROBLEMS;

EID: 84877266254     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2013/583193     Document Type: Article

References (36)

1. Motsa S. S., Sibanda P., Shateyi S., A new spectral-homotopy analysis method for solving a nonlinear second order BVP. Communications in Nonlinear Science and Numerical Simulation 2010 15 9 2293 2302 10.1016/j.cnsns.2009.09.019 MR2602713 ZBL1222.65090
2. Motsa S. S., Sibanda P., Awad F. G., Shateyi S., A new spectral-homotopy analysis method for the MHD Jeffery-Hamel problem. Computers & Fluids 2010 39 7 1219 1225 10.1016/j.compfluid.2010.03.004 MR2645383 ZBL1242.76363
3. Makukula Z. G., Sibanda P., Motsa S. S., A novel numerical technique for two-dimensional laminar flow between two moving porous walls. Mathematical Problems in Engineering 2010 2010 15 528956 10.1155/2010/528956 MR2726293 ZBL1195.76387
4. Motsa S. S., Marewo G. T., Sibanda P., Shateyi S., An improved spectral homotopy analysis method for solving boundary layer problems. Boundary Value Problems 2011 2011, article 3 10.1186/1687-2770-2011-3 MR2821482
5. Shateyi S., Motsa S. S., A new approach for the solution of three-dimensional magnetohydrodynamic rotating flow over a shrinking sheet. Mathematical Problems in Engineering 2010 2010 15 2-s2.0-79251534995 10.1155/2010/586340 586340
6. Sibanda P., Motsa S., Makukula Z., A spectral-homotopy analysis method for heat transfer flow of a third grade fluid between parallel plates. International Journal of Numerical Methods for Heat & Fluid Flow 2012 22 1 4 23 10.1108/09615531211188766 MR2919679
7. Alomari A. K., Noorani M. S. M., Nazar R., Adaptation of homotopy analysis method for the numericanalytic solution of Chen system. Communications in Nonlinear Science and Numerical Simulation 2009 14 2336 2346
8. Ramos J. I., Piecewise homotopy methods for nonlinear ordinary differential equations. Applied Mathematics and Computation 2008 198 1 92 116 10.1016/j.amc.2007.08.030 MR2403933 ZBL1137.65048 (Pubitemid 351337618)
9. Abdulaziz O., Noor N. F. M., Hashim I., Noorani M. S. M., Further accuracy tests on Adomian decomposition method for chaotic systems. Chaos, Solitons and Fractals 2008 36 5 1405 1411 2-s2.0-38649111984 10.1016/j.chaos.2006.09.007 (Pubitemid 351172793)
10. Al-Sawalha M. M., Noorani M. S. M., Hashim I., On accuracy of Adomian decomposition method for hyperchaotic Rössler system. Chaos, Solitons and Fractals 2009 40 4 1801 1807 2-s2.0-65449148390 10.1016/j.chaos.2007.09.062
11. Odibat Z. M., Bertelle C., Aziz-Alaoui M. A., Duchamp G. H. E., A multi-step differential transform method and application to non-chaotic or chaotic systems. Computers & Mathematics with Applications 2010 59 4 1462 1472 10.1016/j.camwa.2009.11.005 MR2591936 ZBL1189.65170
12. + T-cells. Mathematical and Computer Modelling 2011 54 9-10 2132 2138 10.1016/j.mcm.2011.05.022 MR2834617
13. + T-cells. Iranian Journal of Science and Technology A 2011 35 1 9 12 MR2883647
14. Ghorbani A., Saberi-Nadjafi J., A piecewise-spectral parametric iteration method for solving the nonlinear chaotic Genesio system. Mathematical and Computer Modelling 2011 54 1-2 131 139 10.1016/j.mcm.2011.01.044 MR2801872 ZBL1225.65120
15. Genesio R., Tesi A., Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 1992 28 3 531 548 2-s2.0-0026866475 10.1016/0005-1098(92)90177-H
16. Faieghi M. R., Delavari H., Chaos in fractional-order Genesio-Tesi system and its synchronization. Communications in Nonlinear Science and Numerical Simulation 2012 17 2 731 741 10.1016/j.cnsns.2011.05.038 MR2834432 ZBL1239.93020
17. Goh S. M., Noorani M. S. M., Hashim I., Efficacy of variational iteration method for chaotic Genesio system-classical and multistage approach. Chaos, Solitons and Fractals 2009 40 5 2152 2159 2-s2.0-65549135923 10.1016/j.chaos.2007.10.003
18. + T-cells. Mathematical Biosciences 1993 114 1 81 125 2-s2.0-0027457101 10.1016/0025-5564(93)90043-A
19. + T-cells. Mathematical and Computer Modelling 2011 53 5-6 597 603 10.1016/j.mcm.2010.09.009 MR2769431 ZBL1217.65164
20. + T-cells. Istanbul Commerce University Journal of Science 2007 12 39 52
21. + T-cells. Computers & Mathematics with Applications 2011 62 1 118 123 10.1016/j.camwa.2011.04. 058 MR2821813 ZBL1228.65137
22. Doha E. H., Bhrawy A. H., Ezz-Eldien S. S., Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations. Applied Mathematical Modelling 2011 35 12 5662 5672 10.1016/j.apm.2011.05.011 MR2820942 ZBL1228.65126
23. + T-cells. Applied Mathematical Modelling 2012 36 12 5876 5890 10.1016/j.apm.2011.12.021
24. Liao S., Beyond Perturbation: Introduction to the Homotopy Analysis Method 2003 Chapman & Hall/CRC
25. Bataineh A. S., Noorani M. S. M., Hashim I., Series solution of the multispecies Lotka-Volterra equations by means of the homotopy analysis method. Differential Equations and Nonlinear Mechanics 2008 2008 14 816787 MR2425093 ZBL1160.34302
26. Bataineh A. S., Noorani M. S. M., Hashim I., Homotopy analysis method for singular IVPs of Emden-Fowler type. Communications in Nonlinear Science and Numerical Simulation 2009 14 4 1121 1131 10.1016/j.cnsns.2008.02.004 MR2468944 ZBL1221.65197
27. Hashim I., Abdulaziz O., Momani S., Homotopy analysis method for fractional IVPs. Communications in Nonlinear Science and Numerical Simulation 2009 14 3 674 684 10.1016/j.cnsns.2007.09.014 MR2449879 ZBL1221.65277
28. Tan Y., Abbasbandy S., Homotopy analysis method for quadratic Riccati differential equation. Communications in Nonlinear Science and Numerical Simulation 2008 13 3 539 546 2-s2.0-34848880798 10.1016/j.cnsns.2006.06.006 (Pubitemid 47497345)
29. Atkinson K., Han W., Theoretical Numerical Analysis: A Functional Analysis Framework 2009 3rd Springer 10.1007/978-1-4419-0458-4 MR2511061 ZBL1248.62091
30. Guo B.-Y., Kuo P. Y., Spectral Methods and Their Applications 1998 Singapore World Scientific
31. Canuto C., Hussaini M. Y., Quarteroni A., Zang T. A., Spectral Methods in Fluid Dynamics 1988 Berlin, Germany Springer MR917480
32. Welfert B. D., A Remark on Pseudospectral Differentiation Matrices 1992 Tempe, Ariz, USA Department of Mathematics, Arizona State University
33. + T-cells. Mathematical Biosciences 2006 200 1 44 57 10.1016/j.mbs.2005.12.026 MR2211927 ZBL1086.92035
34. Marinca V., Herişanu N., Application of Optimal Homotopy Asymptotic Method for solving nonlinear equations arising in heat transfer. International Communications in Heat and Mass Transfer 2008 35 6 710 715 2-s2.0-43449134670 10.1016/j.icheatmasstransfer.2008.02.010
35. Liao S. J., The Homotopy Analysis Method in Nonlinear Differential Equations 2012 Heidelberg, Germany Springer
36. Dormand J. R., Prince P. J., A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics 1980 6 1 19 26 10.1016/0771-050X(80)90013-3 MR568599 ZBL0448.65045