Numerical solution of the system of nonlinear ordinary differential equations arising in kinetic modeling of lactic acid fermentation and epidemic model

International Journal for Numerical Methods in Biomedical Engineering

Volumn 27, Issue 4, 2011, Pages 585-594

  Kelleci, Alev ^a   Yildirim, Ahmet ^a  

^a EGE UNIVERSITY   (Turkey)

Author keywords

Cell growth; Epidemic model; Fermentation; Homotopy perturbation method; Kinetic modeling; Lactic acid production; Lactose utilization; System of differential equations

Indexed keywords

EPIDEMIC MODELS; HOMOTOPY PERTURBATION METHOD; KINETIC MODELING; LACTIC ACID PRODUCTION; LACTOSE UTILIZATION; SYSTEM OF DIFFERENTIAL EQUATIONS;

BODY FLUIDS; CELL GROWTH; DIFFERENTIATION (CALCULUS); FERMENTATION; GROWTH KINETICS; IGNEOUS ROCKS; LACTIC ACID; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; POPULATION STATISTICS; SUGARS;

EPIDEMIOLOGY;

EID: 79953059225     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.1321     Document Type: Article

References (33)

1. Tango MSA, Ghaly AE. Kinetic modeling of lactic acid production from submerged fermentation of cheese whey. Transactions of the ASAE 1999; 42(6):1791-1800.
2. Tango MSA. Bioconversion of cheese whey to lactic acid in free and immobilized cell systems, Ph.D. Thesis, Dalhousie University, Halifax, Canada, 2000.
3. Biazar J, Tango M, Babolian E, Islam R. Solution of the kinetic modeling of lactic acid fermentation using Adomian decomposition method. Applied Mathematics and Computation 2003; 144:433-439.
4. Jordan DW, Smith P. Nonlinear Ordinary Differential Equations (3rd edn). Oxford University Press: Delhi, 1999.
5. Biazar J. Solution of the epidemic model by Adomian decomposition method. Applied Mathematics and Computation 2006; 173:1101-1106.
6. He JH. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons, and Fractals 2005; 26:695-700.
7. He JH. Homotopy perturbation method for bifurcation of nonlinear problems. International Journal of Nonlinear Science and Numerical Simulation 2005; 6:207.
8. He JH. Homotopy perturbation method for solving boundary value problems. Physics Letters A 2006; 350:87.
9. He JH. Homotopy perturbation technique. Computer Methods in Applied Mechanics and Engineering 1999; 178:257.
10. Yildirim A, Öziş T. Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method. Physics Letters A 2007; 369:70.
11. Yildirim A. Solution of BVPs for fourth-order integro-differential equations by using Homotopy Perturbation Method. Computers and Mathematics with Applications 2008; 56:3175.
12. Yildirim A. He's homotopy perturbation method for nonlinear differential-difference equations. International Journal of Computer Mathematics 2008; DOI: 10.1080/00207160802247646.
13. Yildirim A. The homotopy perturbation method for approximate solution of the modified KdV equation. Zeitschrift für Naturforschung A. A Journal of Physical Sciences 2008; 63a:621.
14. Yildirim A. Application of the homotopy perturbation method for the Fokker-Planck equation. Communications in Numerical Methods in Engineering 2008; DOI: 10.1002/cnm.1200.
15. Dehghan M, Shakeri F. Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method. Physica Scripta 2007; 75:778-787.
16. Shakeri F, Dehghan M. Inverse problem of diffusion equation by He's homotopy perturbation method. Physica Scripta 2007; 75:551-556.
17. Dehghan M, Shakeri F. Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method. Progress in Electromagnetic Research, PIER 2008; 78:361-376.
18. Dehghan M, Shakeri F. Use of He's homotpy perturbation method for solving a partial differential equation arising in modeling of flow in porous media. Journal of Porous Media 2008; 11:765-778.
19. Saadatmandi A, Dehghan M, Eftekhari A. Application of He's homotopy perturbation method for non-linear system of second-order boundary value problems. Nonlinear Analysis: Real World Applications 2009; 10:1912-1922.
20. Dehghan M, Shakeri F. The numerical solution of the second Painleve equation. Numerical Method for Partial Differential Equations 2008; DOI: 10.1002/num.20416.
21. Soltanian F, Dehghan M, Karbassi SM. Solution of the differential-algebraic equations via homotopy perturbation method and their engineering applications. International Journal of Computer Mathematics, DOI: 10.1080/00207160802545908.
22. Saadatmandi A, Dehghan M. Numerical solution of a mathematical model for capillary formation in tumor angiogenesis via the tau method. Communications in Numerical Methods in Engineering 2008; 24:1467-1474.
23. Shakeri F, Dehghan M. Numerical solution of the Klein-Gordon equation via He's variational iteration method. Nonlinear Dynamics 2008; 51:89-97.
24. Dehghan M, Shakeri F. The use of the decomposition procedure of Adomian for solving a delay differential equation arising in electrodynamics. Physica Scripta 2008; 78:1-11. Article No. 065004.
25. Tatari M, Dehghan M. On the convergence of He's variational iteration method. Journal of Computational and Applied Mathematics 2007; 207:121-128.
26. He JH. Recent development of the homotopy perturbation method. Topological Methods in Nonlinear Analysis 2008; 31:205.
27. He JH. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 2006; 20:1141.
28. He JH. New interpretation of homotopy perturbation method. International Journal of Modern Physics B 2006; 20:2561.
29. He JH. An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. International Journal of Modern Physics B 2008; 22:3487.
30. Öziş T, Yildirim A. Comparison between Adomian's method and He's homotopy perturbation method. Computers and Mathematics with Applications 2008; 56(5):1216-1224.
31. He JH, Wu XH. Exp-function method for nonlinear wave equations. Chaos, Soliton, and Fractals 2006; 30:700-708.
32. Makinde OD. On non-perturbative approach to transmission dynamics of infectious diseases with waning immunity. International Journal of Nonlinear Science and Numerical Simulation 2009; 10:451-458.
33. Shou DH, He JH. Application of parameter-expanding method to strongly nonlinear oscillators. International Journal of Nonlinear Science and Numerical Simulation 2007; 8:121-124.