Adomian Decomposition Method for Solving Goursat's Problems

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