A new algorithm for calculating adomian polynomials for nonlinear operators

By Abdul-Majid Wazwaz. Applied Mathematics and Computation, 2000

690 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a42837b82cd65978e462d19a19ab790d5fd4378b

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Citations in the corpus

The variational iteration method: An efficient scheme for handling fractional partial differential equations in fluid mechanics (2009, methodology): “TheAdomian decompositionmethod [13–17] and the variational iterationmethod [18–38] are relatively newapproaches to provide an analytical approximation to linear and nonlinear problems, and they are particularly valuable as tools for scientists and applied mathematicians, because they provide immedia”
Mathematical studies of the solution of Burgers' equations by Adomian decomposition method (2019, background): “25 Comparing (25) and (26) with (1) and (2), the following observations are noticed: ν = 0, g(x) = cos x, and f (x, t) = − sin(x + t) − 1 2 sin 2(x + t).”
Analytical approximate solutions for nonlinear fractional differential equations (2002, methodology): “and for computational purposes other alternative formulas for the An are used [13].”
Numerical methods for nonlinear partial differential equations of fractional order (2008, methodology): “Keywords: Variational iteration method; Adomian decomposition method; Lagrange multiplier; Fractional differential equation; Caputo fractional derivative”
He's Homotopy Perturbation Method for Calculating Adomian Polynomials (2007, methodology): “The An's are the so called Adomian's polynomials which can be calculated using the formula 1 d" 00 " nldX" ^ ' -° Generally speaking the solution procedure of the Adomian's polynomials is remarkably complex and difficult, though there are some alternative approaches to calculating the Adomian's poly”