The numerical solution of special fourth-order boundary value problems by the modified decomposition method

International Journal of Computer Mathematics

Volumn 79, Issue 3, 2002, Pages 345-356

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Adomian polynomials; Boundary value problems of fourth order; Linear and nonlinear problems; Modified decomposition method

Indexed keywords

ADOMIAN POLYNOMIALS; BOUNDARY VALUE PROBLEMS OF FOURTH ORDER; LINEAR AND NONLINEAR PROBLEMS; MODIFIED DECOMPOSITION METHOD;

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; LINEAR SYSTEMS; NONLINEAR SYSTEMS; POLYNOMIALS; PROBLEM SOLVING; RELIABILITY;

BOUNDARY VALUE PROBLEMS;

EID: 18144406990     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160211928     Document Type: Article

References (15)

1. Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, 1994.
2. Adomian, G. (1988). A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135, 501-544.
3. Agarwal, R. P. (1986). Boundary Value Problems for High Ordinary Differential Equations, World Scientific, Singapore.
4. Baldwin, P. (1987). Asymptotic estimates of the eigenvalues of a fourth-order boundary-value problem obtained by using global phase-integral methods, Phil. Thans. R. Soc. Lond. A, 322, 281-305.
5. Chawla, M. M. and Katti, C. P. (1979). Finite difference methods for two-point boundary value problems involving higher order differential equations, BIT, 19, 27-33.
6. Cherrauault, Y., Saccomandi, G. and Some, B. (1992). New results for convergence of Adomian's method applied to integral equations, Math. Comput. Modelling, 16(2), 85-93.
7. Doedel, E. (1979). Finite difference methods for nonlinear two-point boundary-value problems, SIAM J. Numer. Anal., 16, 173-185.
8. Siddiqi, S. S. and Twizell, E. H. (1996). Spline solutions of linear sixth-order boundary value problems, Intern. J. Comp. Math., 60, 295-304.
9. Usmani, R. A. (1977). On the numerical integration of a boundary value problem involving a fourth order linear differential equations, BIT, 17, 227-234.
10. 6) finite difference analogue for the solution of some differential equations occurring in plate-deflection theory, J. Inst. Maths. Applics., 20, 331-333.
11. Usmani, R. A. (1992). The use of quartic splines in the numerical solution of a fourth-order boundary-value problem, Journal of Computational and Applied Mathematics, 44, 187-199.
12. Wazwaz, A. M. (1997). A First Course in Integral Equations, World Scientific, New Jersey.
13. Wazwaz, A. M. (1999). Analytical approximations and Pade' approximants for Volterra's population model, Applied Mathematics and Computation, 100, 13-25.
14. Wazwaz, A. M. (1999). A reliable modification of Adomian's decomposition method, Applied Mathematics and Computation, 102, 77-86.
15. Wazwaz, A. M. (2000). A new algorithm for calculating Adomian polynomials for nonlinear operators, Applied Mathematics and Computation, 111/1, 53-70.