The Adomian decomposition method (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The method was developed from the 1970s to the 1990s by George Adomian, chair of the Center for Applied Mathematics at the University of Georgia.[1]
It is further extensible to stochastic systems by using the Ito integral.[2]
The aim of this method is towards a unified theory for the solution of partial differential equations (PDE); an aim which has been superseded by the more general theory of the homotopy analysis method.[3]
The crucial aspect of the method is employment of the "Adomian polynomials" which allow for solution convergence of the nonlinear portion of the equation, without simply linearizing the system. These polynomials mathematically generalize to a Maclaurin series about an arbitrary external parameter; which gives the solution method more flexibility than direct Taylor series expansion.[4]
^Adomian, G. (1994). Solving Frontier problems of Physics: The decomposition method. Kluwer Academic Publishers.
^Adomian, G. (1986). Nonlinear Stochastic Operator Equations. Kluwer Academic Publishers. ISBN 978-0-12-044375-8.
^Liao, S.J. (2012), Homotopy Analysis Method in Nonlinear Differential Equation, Berlin & Beijing: Springer & Higher Education Press, ISBN 978-3642251313
^Wazwaz, Abdul-Majid (2009). Partial Differential Equations and Solitary Waves Theory. Higher Education Press. p. 15. ISBN 978-90-5809-369-1.
and 15 Related for: Adomian decomposition method information
The Adomiandecompositionmethod (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The method was developed...
(1922–1996), American mathematician Adomiandecompositionmethod for solving differential equations James Adomian (born 1980), American actor and comedian...
optimization Adomiandecompositionmethod, a non-numerical method for solving nonlinear differential equations Domain decompositionmethods in mathematics...
He developed the Adomiandecompositionmethod (ADM) for solving nonlinear differential equations, both ordinary and partial. The method is explained, among...
studied by Ivar Fredholm. A useful method to solve such equations, the Adomiandecompositionmethod, is due to George Adomian. A Fredholm equation is an integral...
Volterra operators. A useful method to solve such equations, the Adomiandecompositionmethod, is due to George Adomian. A linear Volterra integral equation...
friction factor f by using the Adomiandecompositionmethod. The friction factor containing two terms through this method is given as: f L = K 1 + 4 K 2...
Sons. pp. 51–79. ISBN 0-471-59916-6. Adomian, G. (1994). Solving Frontier problems of Physics: The decompositionmethod. Kluwer Academic Publishers. ISBN 9789401582896...
the Steklov Institute of Mathematics George Adomian, mathematician, developer of Adomiandecompositionmethod Tateos Agekian, astrophysicist, one of the...
Steklov Institute of Mathematics George Adomian (1922–1996) – mathematician, developed the Adomiandecompositionmethod (ADM) for solving nonlinear differential...
three quality-of-care dimensions. Cano, J. A. Sánchez (2011). "AdomianDecompositionMethod for a Class of Nonlinear Problems". ISRN Applied Mathematics...
dioxide absorbed into phenyl glycidyl ether solutions by the Adomiandecompositionmethod". Journal of Mathematical Chemistry. 53 (4): 1054–1067. doi:10...
Topics in Multidimensional Linear Systems Theory (2000), 164 p. George Adomian, Nonlinear Stochastic Systems Theory and Applications to Physics, 1989...