Adomian Decomposition Method for Solving Goursat's Problems

.
DOI: 10.4236/am.2011.28134   PDF   HTML     5,391 Downloads   10,641 Views   Citations

Abstract

In this paper, Goursat’s problems for: linear and nonlinear hyperbolic equations of second-order, systems of nonlinear hyperbolic equations and fourth-order linear hyperbolic equations in which the attached conditions are given on the characteristics curves are transformed in such a manner that the Adomian decomposition method (ADM) can be applied. Some examples with closed-form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate this approach is indeed practical and efficient.

Share and Cite:

M. Al-Mazmumy, "Adomian Decomposition Method for Solving Goursat's Problems," Applied Mathematics, Vol. 2 No. 8, 2011, pp. 975-980. doi: 10.4236/am.2011.28134.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] E. Goursat, “A Course in Mathematical Analysis, Vol. 3: Variation of Solutions and Partial Differential Equations of the Second Order and Integral Equations and Calculus of Variations,” Gauthier-Villars, Paris, 1923.
[2] G. Adomian, “Nonlinear Stochastic Operator Equations,” Academic Press, Orlando, 1986.
[3] G. Adomian, “Solving Frontier Problems of Physics: The Decomposition Method,” Kluwer Academic Publishers, Boston, 1994.
[4] G. Adomian and R. Rach, “Transformation of Series,” Applied Mathematics Letters, Vol. 4, No. 4, 1991, pp. 69-71. doi:10.1016/0893-9659(91)90058-4
[5] G. Adomian, R. Rach and R. E. Meyers, “A Modified Decomposition,” Computers & Mathematics with Applications, Vol. 23, No. 1, January 1992, pp. 17-23. doi:10.1016/0898-1221(92)90076-T
[6] G. Adomian and R. Rach, “Inhomogeneous Nonlinear Partial Differential Equations with Variable Coefficients,” Applied Mathematics Letters, Vol. 5, No. 2, March 1992, pp. 11-12. doi:10.1016/0893-9659(92)90101-E
[7] G. Adomian and R. Rach, “Nonlinear Transformation of Series Part II,” Computers & Mathematics with Applications, Vol. 23, No. 10, May 1992, pp. 79-83. doi:10.1016/0898-1221(92)90058-P
[8] G. Adomian and R. Rach, “Modified Decomposition Solution of Nonlinear Partial Differential Equations,” Applied Mathematics Letters, Vol. 5, No. 6, November 1992, pp. 29-30. doi:10.1016/0893-9659(92)90008-W
[9] G. Adomian and R. Rach, “Solution of Nonlinear Partial Differential Equations in One, Two, Three, and four Dimensions,” World Scientific Series in Applicable Analysis, Vol. 2, 1993, pp. 1-13.
[10] G. Adomian and R. Rach, “Modified Decomposition Solution of Linear and Nonlinear Boundary-Value Problems,” Nonlinear Analysis, Vol. 23, No. 5, September 1994, pp. 615-619. doi:10.1016/0362-546X(94)90240-2
[11] G. Adomian and R. Rach, “Analytic Solution of Nonlinear Boundary-Value Problems in Several Dimensions by Decomposition,” Journal of Mathematical Analysis and Applications, Vol. 174, No. 1, 15 March 1993, pp. 118-137. doi:10.1006/jmaa.1993.1105
[12] G. Adomian and R. Rach, “A New Algorithm for Matching Boundary Conditions in Decomposition Solutions,” Applied Mathematics and Computation, Vol. 58, No. 1, September 1993, pp. 61-68. doi:10.1016/0096-3003(93)90012-4
[13] A. Wazwaz, “The Decomposition Method for Approximate Solution of the Goursat Problem,” Applied Mathematics and Computation, Vol. 69, No. 2-3, May 1995, pp. 299-311. doi:10.1016/0096-3003(94)00137-S

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.