The numerical simulation for stiff systems of ordinary differential equations

Computers and Mathematics with Applications

Volumn 54, Issue 7-8, 2007, Pages 1055-1063

  Darvishi, M T ^a   Khani, F ^b   Soliman, A A ^c  

^a RAZI UNIVERSITY   (Iran)

^b ILAM UNIVERSITY   (Iran)

^c SUEZ CANAL UNIVERSITY   (Egypt)

Author keywords

Stiff systems; Systems of differential equations; Variational iteration method

Indexed keywords

COMPUTER SIMULATION; ITERATIVE METHODS; NONLINEAR EQUATIONS; STIFFNESS;

SYSTEMS OF DIFFERENTIAL EQUATIONS; VARIATIONAL ITERATION METHOD;

DIFFERENTIAL EQUATIONS;

EID: 34748920649     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.12.072     Document Type: Article

References (32)

1. He J.H. A new approach to nonlinear Partial Differential Equations. Commun. Non-Linear Sci. Numer. Simul. 2 4 (1997) 230-235
2. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167 (1998) 27-68
3. He J.H. Approximate solution of nonlinear Differential Equations with convolution product nonlinearities. Comput. Methods Appl. Mech. Engrg. 167 (1998) 69-73
4. He J.H. Variational iteration method-a kind of non-linear analytical technique: Some examples. Internat. J. Non-Linear Mech. 34 (1999) 699-708
5. Debtnath L. Nonlinear Partial Differential Equations for Scientists and Engineers (1997), Birkhauser, Boston
6. Wazwaz A.M. Partial Differential Equations Methods and Applications (2002), Rotterdam, Balkema
7. Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 18 (1971) 1192-1194
8. Yan C.T. A simple transformation for nonlinear waves. Phys. Lett. A 224 (1996) 77-82
9. Wang M.L. Exact solution for a compound KdV-Burgers equation. Phys. Lett. A 213 (1996) 279-287
10. Yan Z.Y., and Zhang H.Q. Symbolic computation and new families of exact soliton-like solutions to the integrable Broer-Kaup (BK) equations in (2 + 1)-dimensional spaces. J. Phys. A 34 (2001) 1785-1792
11. Yan Z.Y., and Zhang H.Q. New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water. Phys. Lett. A 285 (2001) 355-362
12. El-Shahed M. Application of He's homotopy perturbation method to Volterra's integro-differential equation. Internat. J. Nonlinear Sci. Numer. Simul. 6 2 (2005) 163-168
13. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Appl. Math. Comput. 26 3 (2005) 695-700
14. He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos Soliton Fractals 26 3 (2005) 827-833
15. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Internat. J. Nonlinear Sci. Numer. Simul. 6 2 (2005) 207-208
16. He J.H. Homotopy perturbation method for solving boundary value problems. Phys. Lett. A 350 1-2 (2006) 87-88
17. Seddiqui A.M., Mahmood R., and Ghori Q.K. Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method. Internat. J. Nonlinear Sci. Numer. Simul. 7 1 (2006) 7-14
18. Seddiqui A.M., Ahmed M., and Ghori Q.K. Couette and Poiseuille flows for non-Newtonian fluids. Internat. J. Nonlinear Sci. Numer. Simul. 7 1 (2006) 15-26
19. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 2-3 (2000) 115-123
20. Marinca V. An approximate solution for one-dimensional weakly nonlinear oscillations. Internat. J. Nonlinear Sci. Numer. Simul. 3 (2002) 107-110
21. Abdou M.A., and Soliman A.A. Variational iteration method for solving Burger's and coupled Burger's equations. J. Comput. Appl. Math. 181 2 (2005) 245-251
22. Abdou M.A., and Soliman A.A. New applications of variational iteration method. Physica D 211 (2005) 1-8
23. Soliman A.A. Numerical simulation of the generalized regularized long wave equation by He's variational iteration method. Math. Comput. Simul. 70 2 (2005) 119-124
24. Soliman A.A. A numerical simulation and explicit solutions of KdV-Burgers' and Lax's seventh-order KdV equations. Chaos Solitons Fractals 29 (2006) 294-302
25. Draganescu Gh.E., and Capalnasan V. Nonlinear relaxation phenomena in polycrystalline solids. Internat. J. Nonlinear Sci. Numer. Simul. 4 (2004) 219-226
26. Mahmood A.S., Casasús L., and Al-Hayani W. The decomposition method for stiff systems of ordinary differential equations. Appl. Math. Comput. 167 (2005) 964-975
27. Inokuti M., Sekine H., and Mura T. General use of the Lagrange multiplier in nonlinear mathematics. In: Nemat-Nassers (Ed). Variational Method in the Mechanics of Solids (1978), Pergamon Press, Oxford 156-162
28. He J.H. Variational iteration method for delay differential equations. Commun. Nonlinear Sci. Numer. Simul. 2 4 (1997) 235-236
29. He J.H., Wan Y.Q., and Gou Q. An iteration formulation for normalized diode characteristics. Int. J. Circuit Theory Appl. 32 6 (2004) 629-632
30. Alt R. A-stable one-step methods with step-size control for stiff systems of ordinary differential equations. J. Comput. Appl. Math. 4 (1978) 29-35
31. Rosenbrock H.H., and Storey C. Computational Techniques for Chemical Engineers (1966), Pergamon Press, New York
32. Wu X.-Y., and Xia J.-L. Two low accuracy methods for stiff systems. Appl. Math. Comput. 123 (2001) 141-153