Comparison between the homotopy perturbation method and the sine-cosine wavelet method for solving linear integro-differential equations

Computers and Mathematics with Applications

Volumn 54, Issue 7-8, 2007, Pages 1162-1168

  Kajani, M Tavassoli ^a   Ghasemi, M ^b   Babolian, E ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b KHARAZMI UNIVERSITY   (Iran)

Author keywords

Homotopy perturbation method; Integro differential equations; Operational matrix; Orthogonal functions; Sine cosine wavelets

Indexed keywords

FUNCTION EVALUATION; INTEGRODIFFERENTIAL EQUATIONS; NUMERICAL METHODS; WAVELET TRANSFORMS;

HOMOTOPY PERTURBATION METHOD; OPERATIONAL MATRIX; ORTHOGONAL FUNCTIONS; SINE-COSINE WAVELETS;

PERTURBATION TECHNIQUES;

EID: 34848832887     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.12.062     Document Type: Article

References (30)

1. He J.H. Asymptotology of homotopy perturbation method. Appl. Math. Comput. 156 (2004) 591-596
2. He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos, Solitons Fractals 26 (2005) 827-833
3. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Numer. Simul. 6 2 (2005) 207-208
4. He J.H. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, Solitons Fractals 19 4 (2005) 847-851
5. Liu H.M. Variational approach to nonlinear electrochemical system. Chaos, Solitons Fractals 23 2 (2005) 573-576
6. Liu H.M. Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method. Int. J. Nonlinear Sci. Numer. Simul. 5 1 (2004) 95-96
7. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167 1-2 (1998) 57-68
8. He J.H. Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput. Methods Appl. Mech. Engrg. 167 1-2 (1998) 69-73
9. He J.H. Variational iteration method: a kind of nonlinear analytical technique: some examples. Int. J. Nonlinear Mech. 34 4 (1999) 699-708
10. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 2-3 (2000) 115-123
11. He J.H., Wan Y.Q., and Guo Q. An iteration formulation for normalized diode characteristics. Int. J. Circ. Theor. Appl. 32 6 (2004) 629-632
12. He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, Solitons Fractals 29 (2006) 108-113
13. He J.H. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillators, Part III: Double series expansion. Int. J. Nonlinear Sci. Numer. Simul. 2 4 (2001) 317-320
14. He J.H. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillators, Part I: Expansion of constant. Int. J. Nonlinear Mech. 37 2 (2002) 309-314
15. He J.H. Modified Lindstedt-Poincare methods for some strongly nonlinear oscillators, Part II: A new transformation. Int. J. Nonlinear Mech. 37 2 (2002) 315-320
16. Liu H.M. Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method. Chaos, Solitons Fractals 23 2 (2005) 577-579
17. El-Shahed M. Application of He's homotopy perturbation method to Volterra's integro-differential equation. Int. J. Nonlinear Sci. Numer. Simul. 6 2 (2005) 163-168
18. He J.H. Some asymptotic methods for strongly nonlinear equations. Int. J. Modern Phys. B 20 (2006) 1141-1199
19. He J.H. A review on some new recently developed nonlinear analytical techniques. Int. J. Nonlinear Sci. Numer. Simul. 1 1 (2000) 51-70
20. Hillermeier C. Generalized homotopy approach to multiobjective optimization. Int. J. Optim. Theory Appl. 110 3 (2001) 557-583
21. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons Fractals 26 (2005) 695-700
22. He J.H. An approximate solution technique depending upon an artificial parameter. Commun. Nonlinear Sci. Simul. 3 2 (2001) 92-97
23. He J.H. Homotopy perturbation technique. Comput Methods Appl. Mech. Engng. 178 3-4 (1999) 257-262
24. He J.H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int. J. Nonlinear Mech. 35 1 (2000) 37-43
25. He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl. Math. Comput. 151 (2004) 287-292
26. He J.H. Comparison of homotopy perturbation method and homotopy analysis method. Appl. Math. Comput. 156 (2004) 527-539
27. Tavassoli Kajani M., Ghasemi M., and Babolian E. Numerical Solution of linear integro-differential equation by using sine-cosine wavelets. Appl. Math. Comput. 180 (2006) 569-574
28. Razzaghi M., and Yousefi S. Sine-Cosine wavelets operational matrix of integration and its applications in the calculus of variations. Int. J. Syst. Sci. 33 (2002) 805-810
29. Gu J.S., and Jiang W.S. The haar wavelets operational matrix of integration. Int. J. Syst. Sci. 27 (1996) 623-628
30. A.M. Wazwaz, A First Course in Integral Equations, New Jersey, 1997