Adomian Polynomial
المؤلف:
Adomian, G
المصدر:
"Linear Stochastic Operators." Ph.D. Dissertation. Los Angeles, CA: University of California, Los Angeles, 1963.
الجزء والصفحة:
...
12-7-2018
3287
Adomian Polynomial
Adomian polynomials decompose a function 
into a sum of components
 |
(1)
|
for a nonlinear operator 
as
 |
(2)
|
There appears to be no well-defined method for constructing a definitive set of polynomials for arbitrary 
, but rather slightly different approaches are used for different specific functions.
One possible set of polynomials is given by
These polynomials have the property that 
depends only on 
, 
, ..., 
, and that the sum of subscripts for the component 
is equal to 
.
REFERENCES:
Adomian, G. "Linear Stochastic Operators." Ph.D. Dissertation. Los Angeles, CA: University of California, Los Angeles, 1963.
Adomian, G. Stochastic Systems. New York: Academic Press, 1983.
Adomian, G. "A New Approach to Nonlinear Partial Differential Equations." J. Math. Anal. Appl. 102, 420-434, 1984.
Adomian, G. Nonlinear Stochastic Operator Equations. Orlando, FL: Academic Press, 1986.
Adomian, G. "A Review of the Decomposition Method in Applied Mathematics." J. Math. Anal. Appl. 135, 501-544, 1988.
Adomian, G. Nonlinear Stochastic Systems Theory and Applications to Physics. Dordrecht, Netherlands: Kluwer, 1989.
Adomian, G. Solving Frontier Problems of Physics: The Decomposition Method. Boston, MA: Kluwer, 1994.
Bellman, R. and Adomian, G. Partial Differential Equations: New Methods for their Treatment and Solution. Dordrecht, Netherlands: Reidel, 1985.
Cherruault, Y. Modèles et mŽthodes mathŽmatiques pour les sciences du vivant. Paris, France: Presses Universitaires de France, 1998.
Rach, R. "A Convenient Computational Form for the Adomian Polynomials." J. Math. Anal. Appl. 102, 415-419, 1984.
Rach, R. C. "A New Definition of the Adomian Polynomials." Kybernetes 37, 910-955, 2008.
Wazwaz, A. M. "A New Algorithm for Calculating Adomian Polynomials for Nonlinear Operators." Appl. Math. Comput. 111, 53-69, 2000.
Wazwaz, A.-M. Partial Differential Equations: Methods and Applications. Lisse, Netherlands: Balkema Publishers, 2002.
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