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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.

has been cited by the following article:

• TITLE: Adomian Decomposition Method for Solving Goursat's Problems

  AUTHORS: Mariam A. Al-Mazmumy

  KEYWORDS: Goursat’s Problem, Linear and Nonlinear Hyperbolic Equation of Second and Fourth-Orders, System of Linear Hyperbolic Equations of Second Order, Adomian Decomposition Method

  JOURNAL NAME: Applied Mathematics, Vol.2 No.8, August 8, 2011

  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.