A new modification of the homotopy perturbation method for linear and nonlinear operators

Applied Mathematics and Computation

Volumn 189, Issue 1, 2007, Pages 746-753

  Odibat, Zaid M ^a  

^a AL BALQA APPLIED UNIVERSITY   (Jordan)

Author keywords

Homotopy perturbation method; Modified homotopy perturbation method

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTION EVALUATION; LINEAR SYSTEMS; NONLINEAR SYSTEMS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

HOMOTOPY PERTURBATION METHOD; MODIFIED HOMOTOPY PERTURBATION METHOD; RAPID CONVERGENCE;

MATHEMATICAL OPERATORS;

EID: 34248375297     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.11.188     Document Type: Article

References (20)

1. He J.H. Homotopy perturbation technique. Comput. Methods Appl. Mech. Eng. 178 (1999) 257-262
2. He J.H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int J. Non-Linear Mech. 35 1 (2000) 37-43
3. El-Shahed M. Application of He's homotopy perturbation method to Volterra's integro-differential equation. Int. J. Nonlinear Sci. Numer. Simulat. 6 2 (2005) 163-168
4. He J.H. The homtopy perturbation method for nonlinear oscillators with discontinuities. Appl. Math. Comput. 151 (2004) 287-292
5. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Numer. Simulat. 6 2 (2005) 207-208
6. He J.H. Periodic solutions and bifurcations of delay-differential equations. Phys. Lett. A 374 4-6 (2005) 228-230
7. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos Solitons Fractals 26 3 (2005) 695-700
8. He J.H. Homotopy perturbation method for solving boundary value problems. Phys. Lett. A 350 1-2 (2006) 87-88
9. Z. Odibat, S. Momani, Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order, Chaos Solitons Fractals, in press.
10. He J.H. Homtopy perturbation method: a new nonlinear analytic technique. Appl. Math. Comput. 135 (2003) 73-79
11. He J.H. Comparison of homtopy perturbation method and homotopy analysis method. Appl. Math. Comput. 156 (2004) 527-539
12. He J.H. Asymptotology by homtopy perturbation method. Appl. Math. Comput. 156 (2004) 591-596
13. He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos Solitons Fractals 26 3 (2005) 827-833
14. Siddiqui A., Mahmood R., and Ghori Q. Thin film flow of a third grade fluid on moving a belt by He's homotopy perturbation method. Int. J. Nonlinear Sci. Numer. Simulat. 7 1 (2006) 7-14
15. Siddiqui A., Ahmed M., and Ghori Q. Couette and Poiseuille flows for non-Newtonian fluids. Int. J. Nonlinear Sci. Numer. Simulat. 7 1 (2006) 15-26
16. He J.H. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20 10 (2006) 1141-1199
17. Abbasbandy S. Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method. Appl. Math. Comput. 172 (2006) 485-490
18. Abbasbandy S. Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method. Appl. Math. Comput. 173 (2006) 493-500
19. Wazwaz A. The modified decomposition method for analytical treatment of differential equations. Appl. Math. Comput. 173 (2006) 165-176
20. Wazwaz A. A new modification of the Adomian decomposition method for linear and nonlinear operators. Appl. Math. Comput. 122 (2001) 393-405