Application of He's homotopy perturbation method for solving the Cauchy reaction-diffusion problem

Computers and Mathematics with Applications

Volumn 57, Issue 4, 2009, Pages 612-618

  Yildirim, Ahmet ^a  

^a EGE UNIVERSITY   (Turkey)

Author keywords

Cauchy reaction diffusion problem; Homotopy perturbation method; Time dependent partial differential equation

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; DIFFUSION; DIFFUSION IN LIQUIDS; HELIUM; IMAGE SEGMENTATION; PARTIAL DIFFERENTIAL EQUATIONS;

CAUCHY REACTION-DIFFUSION PROBLEM; DIFFUSION EQUATIONS; EXACT SOLUTIONS; HOMOTOPY PERTURBATION METHOD; RAPID CONVERGENCES; TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATION;

PERTURBATION TECHNIQUES;

EID: 58349085540     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2008.11.003     Document Type: Article

References (31)

1. Britton N.F. Reaction-Diffusion Equations and Their Applications to Biology (1998), Academic Press/Harcourt Brace Jovanovich Publishers, New York
2. Cantrell R.S., and Cosner C. Spatial ecology via reaction-diffusion equations. Biology. Wiley Series in Mathematical and Computational (2003), Wiley, Chichester
3. Grindrod P. The Theory and Applications of Reaction-Diffusion Equations. second ed. Oxford Applied Mathematics and Computing Science Series (1996), The Clarendon Press/Oxford Univ. Press, New York
4. Smoller J. Shock Waves and Reaction-Diffusion Equations. second ed. Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences) vol. 258 (1994), Springer, New York
5. Lesnic D. The decomposition method for Cauchy reaction-diffusion problems. Applied Mathematics Letters 20 (2007) 412-418
6. M. Dehghan, F. Shakeri, Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem, Journal of Computational and Applied Mathematics, doi:10.1016/j.cam.2007.03.006
7. Bataineh A.S., Noorani M.S.M., and Hashim I. The homotopy analysis method for Cauchy reaction-diffusion problems. Physics Letters A 372 (2008) 613-618
8. Wang S.Q., and He J.H. Variational iteration method for a nonlinear reaction-diffusion process. International Journal of Chemical Reactor Engineering 6 (2008) A37
9. He J.H., and Wu X.H. Exp-function method for nonlinear wave equations. Chaos, Solitons and Fractals 30 (2006) 700-708
10. He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Applied Mathematics and Computation 151 (2004) 287-292
11. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons and Fractals 26 (2005) 695-700
12. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. International Journal of Nonlinear Science and Numerical Simulation 6 (2005) 207-208
13. He J.H. Homotopy perturbation method for solving boundary value problems. Physics Letters A 350 (2006) 87-88
14. He J.H. Homotopy perturbation technique. Computational Methods in Applied Mechanics and Engineering 178 (1999) 257-262
15. He J.H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. International Journal of Non-linear Mechanics 35 (2000) 37-43
16. He J.H. Homotopy perturbation method: A new nonlinear analytical technique. Applied Mathematics and Computation 135 (2003) 73-79
17. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. A note on He's homotopy perturbation method for van der Pol oscillator with very strong nonlinearity. Chaos, Solitons and Fractals 34 (2007) 989-991
18. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. A comparative study of He's homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities. International Journal of Nonlinear Science and Numerical Simulation 8 (2007) 243-248
19. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. Traveling wave solution of Korteweg-de Vries equation using He's homotopy perturbation method. International Journal of Nonlinear Science and Numerical Simulation 8 (2007) 239-242
20. Öziş T., and Yi{dotless}ldi{dotless}ri{dotless}m A. Determination of periodic solution for a u(1/3) force by He' modified Lindstedt-Poincaré method. Journal of Sound and Vibration 301 (2007) 415-419
21. 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
22. Shakeri F., and Dehghan M. Solution of delay equations via a homotopy perturbation method. Mathematical and Computer Modelling 38 (2008) 486-498
23. O. Abdulaziz, I. Hashim, M.S.H. Chowdhury, Solving variational problems by homotopy-perturbation method. International Journal for Numerical Methods in Engineering, doi:10.1002/nme.2509
24. Miansari M., Ganji D.D., and Miansari M. Jacobi elliptic function solutions of the (1+1)-dimensional dispersive long wave equation by homotopy perturbation method. Numerical Methods for Partial Differential Equations 24 (2008) 1361-1370
25. Beléndez A., Pascual C., Ortuño M., Beléndez T., and Gallego S. 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 (2009) 601-610
26. Beléndez A., Pascual C., Beléndez T., and Hernández A. Solution for an anti-symmetric quadratic nonlinear oscillator by a modified He's homotopy perturbation method. Nonlinear Analysis: Real World Applications 10 (2009) 416-427
27. Chowdhury M.S.H., and Hashim I. Application of multistage homotopy-perturbation method for the solutions of the Chen system. Nonlinear Analysis: Real World Applications 10 (2009) 381-391
28. Chowdhury M.S.H., and Hashim I. Solutions of Emden-Fowler equations by homotopy-perturbation method. Nonlinear Analysis: Real World Applications 10 (2009) 104-115
29. He J.H. Recent development of the homotopy perturbation method. Topological Methods in Nonlinear Analysis 31 (2008) 205-209
30. He J.H. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 20 (2006) 1141-1199
31. He J.H. New interpretation of homotopy perturbation method. International Journal of Modern Physics B 20 (2006) 2561-2568