George Adomian
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Mathematics
George Adomian's Degrees
- PhD Mathematics University of California, Berkeley
- Masters Mathematics University of California, Berkeley
- Bachelors Mathematics University of California, Berkeley
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Why Is George Adomian Influential?
(Suggest an Edit or Addition)According to Wikipedia, George Adomian was an American mathematician of Armenian descent who developed the Adomian decomposition method for solving nonlinear differential equations, both ordinary and partial. The method is explained, among other places, in his book Solving Frontier Problems in Physics: The Decomposition Method . He was a faculty member at the University of Georgia from 1966 through 1989. While at UGA, he started the Center for Applied Mathematics. Adomian was also an aerospace engineer.
George Adomian's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Solving Frontier Problems of Physics: The Decomposition Method (1993) (3163)
- A review of the decomposition method in applied mathematics (1988) (1454)
- A review of the decomposition method and some recent results for nonlinear equations (1990) (692)
- Nonlinear Stochastic Operator Equations (1986) (639)
- A new approach to nonlinear partial differential equations (1984) (490)
- Decomposition methods: A new proof of convergence (1993) (477)
- Nonlinear Stochastic Systems Theory and Applications to Physics (1988) (424)
- Inversion of nonlinear stochastic operators (1983) (196)
- Noise terms in decomposition solution series (1992) (179)
- Nonlinear stochastic differential equations (1976) (171)
- Solution of physical problems by decomposition (1994) (164)
- Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition (1993) (160)
- Solving frontier problems of physics : the decomposition methoc [i.e. method] (1994) (145)
- On the solution of algebraic equations by the decomposition method (1985) (132)
- Further remarks on convergence of decomposition method. (1995) (130)
- Convergent series solution of nonlinear equations (1984) (114)
- The diffusion-Brusselator equation (1995) (107)
- On the analytic solution of the lane-emden equation (1995) (106)
- Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations (1990) (101)
- Modified decomposition solution of linear and nonlinear boundary-value problems (1994) (93)
- Modified Adomian Polynomials (1996) (89)
- A new approach to the heat equation — An application of the decomposition method (1986) (85)
- SOLUTIONS OF NONLINEAR P.D.E. (1998) (82)
- A modified decomposition (1992) (80)
- Solution of the Thomas-Fermi equation (1998) (76)
- A global method for solution of complex systems (1984) (70)
- A global method for solution of complex systems (1984) (70)
- Nonlinear stochastic differential delay equations (1983) (58)
- Modification of the decomposition Approach to the Heat Equation (1987) (54)
- Random Operator Equations in Mathematical Physics. I (1970) (51)
- Transformation of series (1991) (50)
- Solving frontier problems modelled by nonlinear partial differential equations (1991) (50)
- A new algorithm for matching boundary conditions in decomposition solutions (1993) (49)
- Nonlinear Klein-Gordon equation (1996) (48)
- An Efficient Methodology for the Physical Sciences (1991) (47)
- Linear Stochastic Operators (1963) (46)
- On composite nonlinearities and the decomposition method (1986) (43)
- Partial Differential Equations: New Methods for Their Treatment and Solution (1984) (43)
- Generalization of adomian polynomials to functions of several variables (1992) (43)
- An analytical solution of the stochastic Navier-Stokes system (1991) (39)
- Linear and nonlinear Schrödinger equations (1991) (39)
- Nonlinear transformation of series—part II (1992) (38)
- Explicit solutions of nonlinear partial differential equations (1997) (38)
- The Ginzburg-Landau equation (1995) (37)
- Numerical integration, analytic continuation, and decomposition (1997) (35)
- Differential equations with singular coefficients (1992) (34)
- Solution of coupled nonlinear partial differential equations by decomposition (1996) (33)
- Linear Random Operator Equations in Mathematical Physics. III (1971) (31)
- On the convergence region for decomposition solutions (1984) (30)
- New contributions to the solution of transport equations in porous media (1996) (29)
- On linear and nonlinear integro-differential equations (1986) (28)
- The Decomposition Method (1989) (28)
- STOCHASTIC SYSTEMS ANALYSIS (1980) (28)
- Modified decomposition solution of nonlinear partial differential equations (1992) (26)
- Cellular systems and aging models (1985) (26)
- Cellular systems and aging models (1985) (26)
- Inversion of stochastic partial differential operators—The linear case (1980) (25)
- Non-perturbative solution of the Klein-Gordon-Zakharov equation (1997) (24)
- Application of the decomposition method to the Navier-Stokes equations (1986) (24)
- Polynomial nonlinearities in differential equations (1985) (24)
- Partial Differential Equations (1987) (24)
- Numerical algorithms and decomposition (1991) (24)
- Solving the mathematical model of neurosciences and medicine (1995) (24)
- STOCHASTIC GREEN'S FUNCTIONS, (1964) (23)
- ALGEBRAIC COMPUTATION AND THE DECOMPOSITION METHOD (1986) (23)
- CHAPTER 5 – Coupled Nonlinear Stochastic Differential Equations (1986) (22)
- Infinite Systems of Differential Equations (1985) (22)
- A new approach to boundary value equations and application to a generalization of Airy's equation (1989) (22)
- A further consideration of partial solutions in the decomposition method (1992) (21)
- Inhomogeneous nonlinear partial differential equations with variable coefficients (1992) (21)
- Applied stochastic processes (1980) (21)
- Stochastic contaminant transport equation in porous media (1998) (21)
- A nonperturbative analytical solution of immune response with time-delays and possible generalization (1996) (21)
- A nonlinear differential delay equation (1983) (20)
- Operator-theoretic solution of stochastic systems (1980) (20)
- The noisy convergence phenomena in decomposition method solutions (1986) (19)
- ON THE SOLUTION OF NONLINEAR DIFFERENTIAL EQUATIONS WITH CONVOLUTION PRODUCT NONLINEARITIES (1986) (19)
- On the solution of partial differential equations with specified boundary conditions (1989) (18)
- On the solution of equations containing radicals by the decomposition method (1985) (18)
- Systems of nonlinear partial differential equations (1986) (17)
- Coupled differential equations and coupled boundary conditions (1985) (17)
- Multiple decompositions for computational convenience (1990) (16)
- Algebraic equations with exponential terms (1985) (16)
- Non-perturbative analytical solution of the general Lotka-Volterra three-species system (1996) (15)
- Nonlinear stochastic dynamical systems in physical problems (1985) (15)
- Nonlinear dissipative wave equations (1998) (15)
- Biological system interactions. (1984) (15)
- The decomposition method for nonlinear dynamical systems (1986) (15)
- Anharmonic oscillator systems (1983) (14)
- Solving nonlinear differential equations with decimal power nonlinearities (1986) (14)
- Numerical solution of differential equations in the deterministic limit of stochastic theory (1981) (14)
- An adaptation of the decomposition method for asymptotic solutions (1988) (14)
- An approach to steady-state solutions (1992) (14)
- The closure approximation in the hierarchy equations (1971) (14)
- Nonlinear differential equations with negative power nonlinearities (1985) (14)
- Analytical solutions for ordinary and partial differential equations (1987) (13)
- Light scattering in crystals (1984) (13)
- Solution of Nonlinear Partial Differential Equations in One, Two, Three, and Four Dimensions (1993) (13)
- On product nonlinearities in stochastic differential equations (1981) (12)
- Nonlinear random vibration (1996) (12)
- Coupled nonlinear stochastic differential equations (1983) (12)
- Semilinear stochastic systems: Analysis with the method of the stochastic Green's function and application in mechanics (1983) (12)
- The stochastic Riccati equation (1980) (11)
- Computation of solutions to the generalized Michaelis-Menton equation (1994) (11)
- The decomposition method applied to stiff systems (1988) (11)
- Nonlinear transport in moving fluids (1993) (11)
- Wave propagation in nonlinear media (1987) (11)
- SYMMETRIZED SOLUTIONS FOR NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS (1981) (11)
- DECOMPOSITION SOLUTION FOR DUFFING AND VAN DER POL OSCILLATORS (1986) (11)
- Application of the decomposition method to inversion of matrices (1985) (11)
- Fisher-Kolmogorov equation (1995) (10)
- Nonlinear oscillations in physical systems (1987) (10)
- Stochastic Green's formula and application to stochastic differential equations (1977) (10)
- Solution of the Navier-Stokes equation—I (1986) (10)
- Closure approximation error in the mean solution of stochastic differential equations by the hierarchy method (1979) (10)
- An investigation of the asymptotic decomposition method for nonlinear equations in physics (1987) (10)
- Self-correcting approximate solution by the iterative method for linear and nonlinear stochastic differential equations (1980) (9)
- Green’s Functions for Partial Differential Equations (1985) (9)
- The KdV Equation (1989) (9)
- On the control of stochastic systems (1981) (9)
- NEW RESULTS IN STOCHASTIC EQUATIONS - THE NONLINEAR CASE (1978) (8)
- Nonlinear plasma response (1985) (8)
- Stochastic Burgers' equation (1995) (8)
- Analytical solution of navier-stokes flow of a viscous compressible fluid (1995) (7)
- Purely nonlinear differential equations (1990) (7)
- A new approach to the Efinger model for a nonlinear quantum theory for gravitating particles (1987) (7)
- On KdV type equations (1997) (7)
- Explicit solutions for differential equations (1987) (7)
- Solution of the Marchuk model of infectious disease and immune response (1986) (7)
- Stochastic differential operator equations with random initial conditions (1977) (7)
- Delayed nonlinear dynamical systems (1995) (7)
- STOCHASTIC OPERATORS AND DYNAMICAL SYSTEMS (1979) (7)
- The fifth-order Korteweg-de Vries equation (1996) (6)
- Smooth polynomial expansions of piecewise-differentiable functions (1989) (6)
- On the solutions of stochastic initial-value problems in continuum mechanics (1985) (6)
- CHAPTER 6 – Delay Equations (1986) (6)
- Random volterra integral equations (1995) (6)
- Generalized nonlinear Schrödinger equation with time-dependent dissipation (1995) (6)
- Analytic solutions for nonlinear equations (1988) (6)
- Solving the nonlinear equations of physics (1988) (6)
- The Kadomtsev-Petviashvili equation (1996) (6)
- ON THE TRICOMI PROBLEM (1986) (5)
- The origin of chaos (1994) (5)
- Analytic solution of nonlinear integral equations of Hammerstein type (1998) (5)
- Application of decomposition to convection-diffusion equations (1988) (5)
- Solution of complex dynamical systems (1990) (5)
- The Navier-Stokes Equations (1989) (5)
- Stochastic water reservoir modeling (1986) (5)
- On Green's function in higher order stochastic differential equations (1982) (5)
- Speculations on possible directions and applications for the decomposition method (1989) (4)
- On the Itô equation (1982) (4)
- A comparison of the iterative method and Picard's successive approximations for deterministic and stochastic differential equations (1981) (4)
- The nikolaevskiy model for nonlinear seismic waves (1995) (4)
- An application of the decomposition method to the matrix Riccati equation in a neutron transport process (1988) (4)
- On integral, differential, and integro‐differential equations, perturbation and averaging methods (1995) (4)
- A new computational approach for inversion of very large matrices (1986) (4)
- A coupled nonlinear system (1986) (4)
- Stochastic nonlinear modeling of fluctuations in a nuclear reactor—a new approach (1981) (4)
- Vibration in offshore structures- part II (1987) (4)
- Solution of nonlinear evolution equations (1994) (4)
- Analytic parametrization and the decomposition method (1989) (4)
- Decomposition solution of nonlinear hyperbolic equations (1990) (4)
- A General Approach for Complex Systems (1988) (3)
- The generalized Kolmogorov-Petrovskii-Piskunov equation (1995) (3)
- Coupled Maxwell equations for electromagnetic scattering (1996) (3)
- Letter sectionComments on a “counterexample” to decomposition (1989) (3)
- The Sine-Gordon, Klein-Gordon, and Korteweg-De Vries equations (1991) (3)
- Random eigenvalue equations (1985) (3)
- The Burger’s Equation (1989) (3)
- Solution of Algebraic Equations (1986) (3)
- Existence of the inverse of a linear stochastic operator (1986) (3)
- Isentropic flow of an inviscid gas (1995) (3)
- On Modelling Physical Phenomena (1994) (3)
- Stabilization of a stochastic nonlinear economy (1982) (2)
- GENERATION OF A STOCHASTIC PROCESS WITH DESIRED FIRST‐ AND SECOND‐ORDER STATISTICS (1981) (2)
- On the existence of solutions for linear and nonlinear stochastic operator equations (1978) (2)
- Solution of Lanchester equation models for combat (1986) (2)
- Erratum: Random Operator Equations in Mathematical Physics. I (1971) (2)
- ON THE MODELING AND ANALYSIS OF A NATIONAL ECONOMY (1983) (2)
- Integral Boundary Conditions (1994) (2)
- Optical propagation in random media (1997) (2)
- Stochastic model for colored noise (1982) (2)
- A CONSTRUCTIVE METHOD FOR LINEAR AND NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS (1979) (2)
- PARTIAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS (1983) (2)
- On the dynamics of a reaction-diffusion system (1997) (2)
- The Burridge-Knopoff model (1996) (2)
- Approximate calculation of Green's functions (1983) (2)
- Nonlinear equations with mixed derivatives (1986) (2)
- Vibration in offshore structures: an analysis for the general nonlinear stochastic case - part 1 (1987) (2)
- Solution of Differential Equations (1986) (1)
- The N-body problem (1993) (1)
- Nonlinear Dispersive or Dissipative Waves (1989) (1)
- The Initial-Value Problem for the Wave Equation (1989) (1)
- Modeling and solving physical problems (1987) (1)
- A general approach to solution of partial differential equation systems (1987) (1)
- The Benjamin-Ono Equation (1989) (1)
- An algorithm for transient dynamic analysis (1985) (1)
- Elliptic equations and decomposition (1988) (1)
- The Decomposition Method for Ordinary Differential Equations (1994) (1)
- Nonlinear hyperbolic initial value problem (1986) (1)
- Propagation in dissipative or dispersive media (1988) (1)
- State-delayed matrix differential-difference equations (1986) (1)
- New approach to the analysis and control of large space structures (1988) (1)
- On nonzero initial conditions in stochastic differential equations (1984) (1)
- Analysis of model equations of gas dynamics (1988) (1)
- The Decomposition Method in Several Dimensions (1994) (0)
- CHAPTER 15 – Postlude (1986) (0)
- Stationarity Theorems for Stochastic Differential Equations (1970) (0)
- Addendum: Linear Random Operator Equations in Mathematical Physics. III (1972) (0)
- The Variation of Characteristic Values and Functions (1985) (0)
- Applications in Physics (1994) (0)
- Existence and uniqueness of statistical measures for solution processes for linear-stochastic differential equations (1982) (0)
- Boundary Conditions at Infinity (1994) (0)
- Stationary conditions for stochastic differential equations (1972) (0)
- Green’s Functions (1985) (0)
- Applications of Modified Decomposition (1994) (0)
- Propagation in stochastic media (1971) (0)
- Quasilinearization and a New Method of Successive Approximations (1985) (0)
- Linear Programming Discovery (1979) (0)
- Note on orthonormal expansions (1974) (0)
- CHAPTER 2 – Operator Equations and the Decomposition Method (1986) (0)
- Adaptive Grids and Nonlinear Equations (1985) (0)
- CHAPTER 14 – On Systems of Nonlinear Partial Differential Equations (1986) (0)
- Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations (1989) (0)
- A new algorithm for solution of the harmonic oscillator by decomposition (1994) (0)
- Boundary-Value Problems with Closed Irregular Contours or Surfaces (1994) (0)
- A new approach to Burgers' equation (1988) (0)
- A new approach to solution of the maxwell equations (1995) (0)
- A non-perturbative solution of N-Body dynamics (1996) (0)
- Radiative aspects of lunar materials Final report (1968) (0)
- Research on Initial and Boundary Conditions for Differential and Partial Differential Equations (1989) (0)
- CHAPTER 10 – Algebraic Equations (1986) (0)
- A stochastic model for signal processing and propagation (1981) (0)
- The Sine-Gordon Equation (1989) (0)
- The Euler-Lagrange Equations and Characteristics (1985) (0)
- Erratum: Linear Random Operator Equations in Mathematical Physics. I (1971) (0)
- Heat Flow and Diffusion (1989) (0)
- Effects of Nonlinearity and Linearization (1989) (0)
- Decomposition Solutions for Neumann Boundary Conditions (1994) (0)
- CHAPTER 12 – Boundary Conditions (1986) (0)
- Solution of the Duffing Equation (1994) (0)
- The dissipative sine-Gordon equation (1996) (0)
- Dynamical Systems Involving Uncertainty (1976) (0)
- Nonlinear Parabolic Equations (1985) (0)
- CHAPTER 8 – Random Eigenvalue Equations (1986) (0)
- Physiological Sciences-Biological system interactions ( modeling / delayed effects / coupled equations and coupled systems / oscillations and anharmonic oscillators / cellular or population growth ) (0)
- Absolute Value Boundedness, Operator Decomposition, and Stochastic Media and Equations (1973) (0)
- Semilinear wave equations (1987) (0)
- High standards and education (1969) (0)
- The Itô Equation and a General Stochastic Model for Dynamical Systems (1985) (0)
- Nonlinear Partial Differential Equations and the Decomposition Method (1985) (0)
- A stochastic approach to inverse scattering in geophysical layers (1984) (0)
- CHAPTER 3 – Expansion of Nonlinear Terms: The An Polynomials (1986) (0)
- The Nonlinear Schrödinger Equation and the Generalized Schrödinger Equation (1989) (0)
- A class of nonlinear relativistic partial differential equations in elementary particle theory (1993) (0)
- The Hadamard Variational Formula (1985) (0)
- The Heat Equation (1985) (0)
- A New Approach to the Analysis and Control of Large Space Structures. Phase 1. (1988) (0)
- CHAPTER 13 – Integral and Integro-Differential Operators (1986) (0)
- Signal processing in a randomly time varying system. (1972) (0)
- Corrigenda and comment on “A general approach to solution of partial differential equation systems” (1988) (0)
- CHAPTER 7 – Discretization versus Decomposition (1986) (0)
- Discretization, decomposition, and supercomputers (1985) (0)
- Solution of generic nonlinear oscillators (1994) (0)
- Monotone Convergence and Positive Operators (1985) (0)
- NEW APPROACHES TO SOLUTION OF NATIONAL ECONOMY MODELS AND BUSINESS CYCLES (1985) (0)
- More on tenure (1978) (0)
- CHAPTER 11 – Convergence (1986) (0)
- Analytic solutions for time-dependent Schrödinger equations with linear of nonlinear Hamiltonians (1994) (0)
- The Three Dimensional Potential Equation (1985) (0)
- Demand for good physicists (1978) (0)
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