Approximate analytical solution of fourth order boundary value problems

Numerical Algorithms

Volumn 40, Issue 1, 2005, Pages 67-78

  Al Hayani, Waleed ^a   Casasús, Luis ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

Adomian's polynomials; Boundary value problems (BVPs); Decomposition method; Pad approximants

Indexed keywords

EID: 22944466379     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11075-005-3569-9     Document Type: Article

References (28)

1. K. Abbaoui and Y. Cherruault, Convergence of Adomian's method applied to nonlinear equations, Math. Comput. Modelling 20(9) (1994) 60-73.
2. K. Abbaoui and Y. Cherruault, Convergence of Adomian's method applied to differential equations, Math. Comput. Modelling 28(5) (1994) 103-109.
3. K. Abbaoui and Y. Cherruault, New ideas for proving convergence of decomposition methods, Computers Math. Appl. 29(7) (1995) 103-108.
4. K. Abbaoui and Y. Cherruault, The decomposition method: New proof of convergence, in: 11th Internat. Congress of Cybernetics and Systems, Brunel University, Uxbridge, Middlesex, UK (August 1999).
5. K. Abbaoui, M.J. Pujol, Y. Cherruault, N. Himoun and P. Grimalt, A new formulation of Adomian method: Convergence result, Internat. J. Systems Cybernet. 30(9) (2001) 1183-1191.
6. G. Adomian, Stochastic Systems (Academic Press, New York, 1983).
7. G. Adomian, Nonlinear Stochastic Operator Equations (Academic Press, New York, 1986).
8. G. Adomian, Nonlinear Stochastic Systems Theory and Applications to Physics (Kluwer Academic, Dordrecht, 1989).
9. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method (Kluwer Academic, Dordrecht, 1994).
10. E.A. Al-Said and M.A. Noor, Quartic spline method for solving fourth order obstacle boundary value problems, J. Comput. Appl. Math. 143 (2002) 107-116.
11. T. Badredine, K. Abbaoui and Y. Cherruault, Convergence of Adomian's method applied to integral equations, Internat. J. Systems Cybernet. 28(5) (1999) 55-56.
12. L. Casasús and W. Al-Hayani, The method of Adomian for a nonlinear boundary value problem with a small parameter, in: Alhambra 2000, A Joint Mathematical European-Arabic Conference, University of Granada, Spain (2000) pp. 116-121.
13. Y. Cherruault and G. Adomian, Decomposition methods: A new proof of convergence, Math. Comput. Modelling 18(12) (1993) 103-106.
14. G. Choudury and P. Korman, Computation of solutions of nonlinear boundary value problems, Computers Math. Appl. 22(8) (1991) 49-55.
15. Y. Cherruault, Modèles et Méthodes Mathématiques pour les Sciences du Vivant (P.U.F., 1998).
16. M. El-Gamel, S.H. Behiry and H. Hashish, Numerical method for the solution of special nonlinear fourth-order boundary value problems, Appl. Math. Comput. 145 (2003) 717-734.
17. S. Guellal and Y. Cherruault, Practical formula for calculation of Adomian's polynomials and application to the convergence of the decomposition method, Internat. J. Bio-Medical Comput. 36 (1994) 223-228.
18. N. Himoun, K. Abbaoui and Y. Cherruault, New results of convergence of Adomian's method, Internat. J. Systems Cybernet. 28(4) (1999) 42.
19. M.K. Jain, Numerical Solution of Differential Equations (Wiley Eastern, New Delhi, 1979).
20. M. Kumar, A fourth-order finite difference method for a class of singular two-point boundary value problems, Appl. Math. Comput. 133 (2002) 539-545.
21. B. Liu, Positive solutions of fourth-order two point boundary value problems, Appl. Math. Comput. 148 (2004) 407-420.
22. R.Z. Ouedraogo, Y. Cherruault and K. Abbaoui, Convergence of Adomian's method applied to algebraic equations, Internat. J. Systems Cybernet. 29(910) (2000) 1298-1305.
23. E. Rovderová and J. Rovder, On the number of solutions of a fourth-order boundary value problem, in: Proc. of the 2nd World Congress of Nonlinear Analysis, Special Issue of Nonlinear Anal., Theory Methods Appl. 30(8) (1997) 4875-4880.
24. M. Ruyun, Z. Jihui and F. Shengmao, The method of lower and upper solutions for fourth-order two-point boundary value problems, J. Math. Anal. Appl. 215 (1997) 415-422.
25. V. Shanthi and N. Ramanujam, Asymptotic numerical methods for singularly perturbed fourth-order ordinary differential equations of reaction-diffusion type, Computers Math. Appl. 46 (2003) 463-478.
26. V. Shanthi and N. Ramanujam, Computational methods for reaction-diffusion problems for fourth order ordinary differential equations with a small parameter at the highest derivative, Appl. Math. Comput. 147 (2004) 97-113.
27. A.M. Wazwaz, A reliable modification of Adomian decomposition method, Appl. Math. Comput. 102 (1999) 77-86.
28. A.M. Wazwaz, Approximate solutions to boundary value problems of higher order by the modified decomposition method, Computers Math. Appl. 40 (2000) 679-691.