On the applicability of the Adomian method to initial value problems with discontinuities

DOI10.1016/j.aml.2005.03.004zbMath1090.34502OpenAlexW1979062156MaRDI QIDQ812741

Waleed Al-Hayani, Luis Casasús

Publication date: 24 January 2006

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2005.03.004

zbMATH Keywords

Heaviside functiondecomposition methodinitial value problemsAdomian's polynomialsDirac delta function

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Discontinuous ordinary differential equations (34A36)

Cites Work

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• A reliable modification of Adomian decomposition method
• Solving frontier problems of physics: the decomposition method
• Decomposition methods: A new proof of convergence
• Convergence of Adomian's method applied to differential equations
• Convergence of Adomian's method applied to nonlinear equations
• An analytic study on the third-order dispersive partial differential equations.
• A new algorithm for calculating Adomian polynomials for nonlinear operators
• Nonlinear equations with mixed derivatives
• Inversion of nonlinear stochastic operators
• The decomposition method for ordinary differential equations with discontinuities
• An analytic study of Fisher's equation by using Adomian decomposition method
• New ideas for proving convergence of decomposition methods
• An algorithm for solving a nonlinear integro-differential equation

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