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Convergence of Adomian's method applied to nonlinear equations
In this paper, we give a proof of Adomian's method using only some properties of the nonlinear function, and we apply these results to some concrete problems.
Convergence of Adomian's method
We propose general conditions and a new formulation for proving the convergence of Adomian's method for the numerical resolution of nonlinear functional equations depending on one or severalExpand
Decomposition methods: A new proof of convergence
We propose a new convergence proof of Adomian's technique based on properties of convergent series. Then we deduce some results about the speed of convergence of this method allowing us to solveExpand
Convergence of Adomian's method applied to differential equations
This paper deals with a new proof of convergence of Adomian's method applied to differential equations. We also give new formulae and properties, and we suggest a simple computational form forExpand
Characterization and generation of α-dense curves
Abstract If a curve ranges through a cube H = Π n i =1 [ a i , b i ] so that, for every point x ∈ H , there is at least a point in the curve at a distance not greater than a positive number α, theExpand
INTRODUCTION TO OPTIMAL CONTROL THEORY
TLDR
Optimal Control theory is concerned with the problem of how to govern systems. Expand
Convergence of Adomian's Method
Adomian has developed a numerical technique using special kinds of polynomials for solving non‐linear functional equations. General conditions and a new formulation are proposed for proving theExpand
New results for convergence of Adomian's method applied to integral equations
This paper deals with a new proof of convergence of Adomian's method. Series substition properties are used. We give numerical applications to nonlinear integral equations.
New numerical study of Adomian method applied to a diffusion model
We prove in this paper the convergence of Adomian method applied to linear or non‐linear diffusion equations. The results show that the convergence of this method is not influenced by the choice ofExpand
Further remarks on convergence of decomposition method.
TLDR
The decomposition method solves a wide class of nonlinear functional equations using a series solution with rapid convergence. Expand
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