Adomian, G.
Overview
Works:  32 works in 134 publications in 2 languages and 3,288 library holdings 

Genres:  Conference papers and proceedings Periodicals 
Roles:  Author, Editor 
Publication Timeline
.
Most widely held works by
G Adomian
Stochastic systems by
G Adomian(
)
20 editions published between 1982 and 1987 in English and Russian and held by 1,535 WorldCat member libraries worldwide
20 editions published between 1982 and 1987 in English and Russian and held by 1,535 WorldCat member libraries worldwide
Partial differential equations : new methods for their treatment and solution by
Richard Bellman(
Book
)
19 editions published between 1984 and 1985 in English and held by 518 WorldCat member libraries worldwide
The purpose of this book is to present some new methods in the treatment of partial differential equations. Some of these methods lead to effective numerical algorithms when combined with the digital computer. Also presented is a useful chapter on Green's functions which generalizes, after an introduction, to new methods of obtaining Green's functions for partial differential operators. Finally some very new material is presented on solving partial differential equations by Adomian's decomposition methodology. This method can yield realistic computable solutions for linear or non linear cases even for strong nonlinearities, and also for deterministic or stochastic cases  again even if strong stochasticity is involved. Some interesting examples are discussed here and are to be followed by a book dealing with frontier applications in physics and engineering. In Chapter I, it is shown that a use of positive operators can lead to monotone convergence for various classes of nonlinear partial differential equations. In Chapter II, the utility of conservation technique is shown. These techniques are suggested by physical principles. In Chapter III, it is shown that dyn~mic programming applied to variational problems leads to interesting classes of nonlinear partial differential equations. In Chapter IV, this is investigated in greater detail. In Chapter V, we show. that the use of a transformation suggested by dynamic programming leads to a new method of successive approximations
19 editions published between 1984 and 1985 in English and held by 518 WorldCat member libraries worldwide
The purpose of this book is to present some new methods in the treatment of partial differential equations. Some of these methods lead to effective numerical algorithms when combined with the digital computer. Also presented is a useful chapter on Green's functions which generalizes, after an introduction, to new methods of obtaining Green's functions for partial differential operators. Finally some very new material is presented on solving partial differential equations by Adomian's decomposition methodology. This method can yield realistic computable solutions for linear or non linear cases even for strong nonlinearities, and also for deterministic or stochastic cases  again even if strong stochasticity is involved. Some interesting examples are discussed here and are to be followed by a book dealing with frontier applications in physics and engineering. In Chapter I, it is shown that a use of positive operators can lead to monotone convergence for various classes of nonlinear partial differential equations. In Chapter II, the utility of conservation technique is shown. These techniques are suggested by physical principles. In Chapter III, it is shown that dyn~mic programming applied to variational problems leads to interesting classes of nonlinear partial differential equations. In Chapter IV, this is investigated in greater detail. In Chapter V, we show. that the use of a transformation suggested by dynamic programming leads to a new method of successive approximations
Applied stochastic processes : [proceedings] by
G Adomian(
Book
)
21 editions published between 1978 and 2015 in English and Undetermined and held by 368 WorldCat member libraries worldwide
Applied Stochastic Processes is a collection of papers dealing with stochastic processes, stochastic equations, and their applications in many fields of science. One paper discusses stochastic systems involving randomness in the system itself that can be a large dynamical multiinput, multioutput system. Examples of a large system are the national economy of a major country or when an acoustic wave is propagating as in the atmosphere, ocean, or sea. Another paper proves that only the average properties of the molecules of biology can be measured with precision in the test tube; and disputes a
21 editions published between 1978 and 2015 in English and Undetermined and held by 368 WorldCat member libraries worldwide
Applied Stochastic Processes is a collection of papers dealing with stochastic processes, stochastic equations, and their applications in many fields of science. One paper discusses stochastic systems involving randomness in the system itself that can be a large dynamical multiinput, multioutput system. Examples of a large system are the national economy of a major country or when an acoustic wave is propagating as in the atmosphere, ocean, or sea. Another paper proves that only the average properties of the molecules of biology can be measured with precision in the test tube; and disputes a
Nonlinear stochastic operator equations by
G Adomian(
Book
)
11 editions published between 1986 and 2015 in English and Undetermined and held by 333 WorldCat member libraries worldwide
Nonlinear Stochastic Operator Equations deals with realistic solutions of the nonlinear stochastic equations arising from the modeling of frontier problems in many fields of science. This book also discusses a wide class of equations to provide modeling of problems concerning physics, engineering, operations research, systems analysis, biology, medicine. This text discusses operator equations and the decomposition method. This book also explains the limitations, restrictions and assumptions made in differential equations involving stochastic process coefficients (the stochastic operator case)
11 editions published between 1986 and 2015 in English and Undetermined and held by 333 WorldCat member libraries worldwide
Nonlinear Stochastic Operator Equations deals with realistic solutions of the nonlinear stochastic equations arising from the modeling of frontier problems in many fields of science. This book also discusses a wide class of equations to provide modeling of problems concerning physics, engineering, operations research, systems analysis, biology, medicine. This text discusses operator equations and the decomposition method. This book also explains the limitations, restrictions and assumptions made in differential equations involving stochastic process coefficients (the stochastic operator case)
Nonlinear stochastic systems theory and applications to physics by
G Adomian(
Book
)
11 editions published between 1988 and 2001 in English and held by 243 WorldCat member libraries worldwide
11 editions published between 1988 and 2001 in English and held by 243 WorldCat member libraries worldwide
Solving frontier problems of physics : the decomposition methoc [i.e. method] by
G Adomian(
Book
)
18 editions published between 1994 and 2011 in English and held by 228 WorldCat member libraries worldwide
The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundaryvalue problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationallyintensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundaryvalue problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations
18 editions published between 1994 and 2011 in English and held by 228 WorldCat member libraries worldwide
The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundaryvalue problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationallyintensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundaryvalue problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations
Stochastic systems by
G Adomian(
)
2 editions published in 1983 in English and held by 24 WorldCat member libraries worldwide
2 editions published in 1983 in English and held by 24 WorldCat member libraries worldwide
Linear stochastic operators by
G Adomian(
)
4 editions published between 1961 and 1963 in English and held by 10 WorldCat member libraries worldwide
4 editions published between 1961 and 1963 in English and held by 10 WorldCat member libraries worldwide
Partial differential equations : New methods for their treatment and solution by
Richard Bellman(
Book
)
1 edition published in 1985 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1985 in English and held by 3 WorldCat member libraries worldwide
Stohastičeskie sistemy by
G Adomian(
Book
)
2 editions published in 1987 in Russian and Undetermined and held by 2 WorldCat member libraries worldwide
2 editions published in 1987 in Russian and Undetermined and held by 2 WorldCat member libraries worldwide
Book of abstracts : third International Conference on Mathematical Modeling, an interdisciplinary integrative forum for mathematical
modeling in engineering, biological, medical, environmental, social and other sciences, Los Angeles, California, U.S.A. by International Conference on Mathematical Modelling(
Book
)
2 editions published in 1981 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1981 in English and held by 2 WorldCat member libraries worldwide
Bellman memorial issue(
Book
)
1 edition published in 1986 in Undetermined and held by 2 WorldCat member libraries worldwide
1 edition published in 1986 in Undetermined and held by 2 WorldCat member libraries worldwide
The closure approximation in the hierarchy equations by
G Adomian(
Book
)
2 editions published between 1970 and 1971 in English and held by 2 WorldCat member libraries worldwide
The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the 'selfconsistent field' approximation in nonequilibrium statistical mechanics is clarified. (Author)
2 editions published between 1970 and 1971 in English and held by 2 WorldCat member libraries worldwide
The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the 'selfconsistent field' approximation in nonequilibrium statistical mechanics is clarified. (Author)
Linear random operator equations in mathematical physics by
G Adomian(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
STOCHASTIC GREEN'S FUNCTIONS(
Book
)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
A new approach is presented to the theory of random equations for use in physical problems. After a basic summary of necessary ideas and definitions relevant to stochastic processes, the paper develops a linear transformation theory which allows the operators as well as the operand to be stochastic. The statistics of a transformed process are found in terms of the known statistics of the original process and a 'stochastic Green's function'. The problem of determining a stochastic Green's function for a linear stochastic differential operator is studied. (Detailed results for the random sampling of a random process have been obtained in the author's dissertation but only an initial form is shown in the paper to show the nature of the integral kernel or stochastic Green's function.) Interesting applications to 'systems' problems, quantum theory, and propagation in random media are briefly suggested
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
A new approach is presented to the theory of random equations for use in physical problems. After a basic summary of necessary ideas and definitions relevant to stochastic processes, the paper develops a linear transformation theory which allows the operators as well as the operand to be stochastic. The statistics of a transformed process are found in terms of the known statistics of the original process and a 'stochastic Green's function'. The problem of determining a stochastic Green's function for a linear stochastic differential operator is studied. (Detailed results for the random sampling of a random process have been obtained in the author's dissertation but only an initial form is shown in the paper to show the nature of the integral kernel or stochastic Green's function.) Interesting applications to 'systems' problems, quantum theory, and propagation in random media are briefly suggested
Bellman memorial issue dedicated to Nina Bellman(
Book
)
2 editions published in 1986 in Undetermined and English and held by 1 WorldCat member library worldwide
2 editions published in 1986 in Undetermined and English and held by 1 WorldCat member library worldwide
Theory of random systems by
G Adomian(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
Partial differential equations. by
Richard Bellman(
Book
)
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
A proposed Institute of Mathematics by
G Adomian(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
Linear random operator equations in mathematical physics by
G Adomian(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Bellman, Richard 19201984 Honoree Author
 Applied Stochastic Processes Conference. <1978, Athens, Ga.>.
 Avula, Xavier J. R.
 University of MissouriRolla
 GEORGIA UNIV ATHENS Dept. of STATISTICS
 Riganti, R.
 PENNSYLVANIA STATE UNIV UNIVERSITY PARK ORDNANCE RESEARCH LAB
 Elrod, M.
 Volkov, N.G. Translator
 Bellomo, N.
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Associated Subjects
Canada College administrators College teachers Consultants Decomposition method Differential equations Differential equations, Partial EducationCurricula Engineers Executives GeorgiaAthens Global analysis (Mathematics) Linear operators Mathematical models Mathematical physics Mathematical statistics Mathematics MathematicsResearch MathematicsStudy and teaching (Higher) Model theory Nonlinear theories Operator equations Physics Potential theory (Mathematics) Probabilities Research Scientists Stochastic differential equations Stochastic processes Stochastic systems United States University of Georgia