Solving nonlocal boundary value problems for first- and second-order differential equations by the Adomian decomposition method

Kybernetes

Volumn 42, Issue 4, 2013, Pages 641-664

  Bougoffa, Lazhar ^a   Rach, Randolph C ^b  

^a AL IMAM MOHAMMAD IBN SAUD ISLAMIC UNIVERSITY IMSIU   (Saudi Arabia)

^b ADME   (United States)

Author keywords

Adomian decomposition method; Adomian polynomials; Differential equations; Nonlinear differential equations; Nonlocal boundary value problems; Polynomials; Sturm Liouville boundary value problems

Indexed keywords

EID: 84879937731     PISSN: 0368492X     EISSN: None     Source Type: Journal    
DOI: 10.1108/K-09-2012-0045     Document Type: Article

References (28)

1. Adomian, G. (1986a), "A new approach to the heat equation - an application of the decomposition method" in Journal of Mathematical Analysis and Applications, Vol. 113, No. 1, pp. 202-209.
2. Adomian, G. (1986b), Nonlinear Stochastic Operator Equations, Academic, Orlando, FL.
3. Adomian, G. (1994a), Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers, Dordrecht.
4. Adomian, G. (1994b), Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic, Dordrecht.
5. Adomian, G., Rach, R.C. (1991), "Transformation of series" in Applied Mathematics Letters, Vol. 4, No. 4, pp. 69-71.
6. Adomian, G., Rach, R.C. (1994), "Modified decomposition solution of linear and nonlinear boundary-value problems" in Nonlinear Analysis: Theory, Methods and Applications, Vol. 23, No. 5, pp. 615-619.
7. Adomian, G., Rach, R.C., Meyers, R.E. (1992), "A modified decomposition" in Computers and Mathematics with Applications, Vol. 23, No. 1, pp. 17-23.
8. Bougoffa, L., Al-Haqbani, M., Rach, R.C. (2012), "A convenient technique for solving integral equations of the first kind by the Adomian decomposition method" in Kybernetes, Vol. 41, No. 1, pp. 145-156.
9. Bougoffa, L., Rach, R.C., Mennouni, A. (2011), "An approximate method for solving a class of weakly-singular Volterra integro-differential equations" in Applied Mathematics and Computation, Vol. 217, No. 22, pp. 8907-8913.
10. Duan, J.H., Rach, R.C., Baleanu, D., Wazwaz, A.M. (2012), "A review of the Adomian decomposition method and its applications to fractional differential equations" in Communications in Fractional Calculus, Vol. 3, No. 2, pp. 73-99.
11. Duan, J.S. (2011), "Convenient analytic recurrence algorithms for the Adomian polynomials" in Applied Mathematics and Computation, Vol. 217, No. 13, pp. 6337-6348.
12. Duan, J.S., Rach, R.C. (2011), "A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations" in Applied Mathematics and Computation, Vol. 218, No. 8, pp. 4090-4118.
13. Etgen, G.J., Tefteller, S.C. (1972), "Second order differential equations with general boundary conditions" in SIAM Journal of Mathematical Analysis, Vol. 3, No. 3, pp. 512-519.
14. Lesnic, D. (2001), "A computational algebraic investigation of the decomposition method for time-dependent problems" in Applied Mathematics and Computation, Vol. 119, Nos 2/3, pp. 197-206.
15. Patrick, W.D. (1973), "Second order linear differential equations with 2-point and integral boundary conditions", Naval Postgraduate School, Monterey, CA, Thesis.
16. Rach, R.C., Wazwaz, A.M., Duan, J.S. (2013), "A reliable modification of the Adomian decomposition method for higher-order nonlinear differential equations" in Kybernetes, Vol. 42, No. 2, pp. 282-308.
17. von Mises, R. (1912) in Festschrift Heinrich Weber, Teubner, Leipzig, pp. 252-282.
18. Wazwaz, A.M. (1999), "A reliable modification of Adomian decomposition method" in Applied Mathematics and Computation, Vol. 102, No. 1, pp. 77-86.
19. Wazwaz, A.M. (2009), Partial Differential Equations and Solitary Waves Theory, Higher Education Press, Beijing.
20. Adomian, G. (1987), "Modification of decomposition approach to the heat equation" in Journal of Mathematical Analysis and Applications, Vol. 124, No. 1, pp. 290-291.
21. Adomian, G., Rach, R.C. (1992a), "Inhomogeneous nonlinear partial differential equations with variable coefficients" in Applled Mathematics Letters, Vol. 5, No. 2, pp. 11-12.
22. Adomian, G., Rach, R.C. (1992b), "Modified decomposition solution of nonlinear partial differential equations" in Applied Mathematics Letters, Vol. 5, No. 6, pp. 29-30.
23. Adomian, G., Rach, R.C. (1992c), "Nonlinear transformation of series - part II" in Computers and Mathematics with Applications, Vol. 23, No. 10, pp. 79-83.
24. Adomian, G., Rach, R.C. (1993a), "Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition" in Journal of Mathematical Analysis and Applications, Vol. 174, No. 1, pp. 118-137.
25. Adomian, G., Rach, R.C. (1993b), "Solution of nonlinear partial differential equations in one, two, three, and four dimensions" in World Scientific Series in Applicable Analysis, Vol. 2, pp. 1-13.
26. Bougoffa, L., Rach, R.C., Mennouni, A. (2011), "A convenient technique for solving linear and nonlinear Abel integral equations by the Adomian decomposition method" in Applied Mathematics and Computation, Vol. 218, No. 5, pp. 1785-1793.
27. Wazwaz, A.M. (1997), "Equality of partial solutions in the decomposition method for partial differential equations" in International Journal of Computer Mathematics, Vol. 65, Nos 3/4, pp. 293-308.
28. Wazwaz, A.M., El-Sayed, S.M. (2001), "A new modification of the Adomian decomposition method for linear and nonlinear operators" in Applied Mathematics and Computation, Vol. 122, No. 23, pp. 393-405.