Solving a class of linear partial differential equations with Dirichlet‐boundary conditions by the Adomian method

DOI10.1108/03684920410545270zbMath1058.65133OpenAlexW2091440161MaRDI QIDQ4832508

Mohamed Benabidallah, Yves Cherruault

Publication date: 4 January 2005

Published in: Kybernetes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1108/03684920410545270

zbMATH Keywords

optimal controlDirichlet problemnumerical examplesPoisson equationAdomian decomposition method

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Decomposition methods (49M27) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (1)

Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions

Cites Work

• Convergent series solution of nonlinear equations
• New ideas for proving convergence of decomposition methods
• Practical formulae for the calculus of multivariable Adomian polynomials
• Analytic solution of nonlinear boundary-value problems in serveral dimensions by decomposition
• A new formulation of Adomian method
• Convergence of Adomian’s method applied to algebraic equations
• New results of convergence of Adomian’s method
• Analytical solution of nonlinear partial differential equations of physics
• New results for the Adomian method
• New numerical study of Adomian method applied to a diffusion model
• Using the Adomian method for solving a class of boundary differential systems
• Application of the Adomian method for solving a class of boundary problems

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