Partial differential equations with integral boundary conditions

AbstractHyperbolic nonconservative partial differential equations, such as the Von Foerster system, in which boundary conditions may depend upon the dependent variable (integral boundary conditions, for example) are solved by an approximation method based on similar work of the author for (nonlinear stochastic) ordinary differential equations

Absolute Value Boundedness, Operator Decomposition, and Stochastic Media and Equations

The research accomplished during this period is reported. Published abstracts and technical reports are listed. Articles presented include: boundedness of absolute values of generalized Fourier coefficients, propagation in stochastic media, and stationary conditions for stochastic differential equations

Solving the nonlinear equations of physics

AbstractApplication of the decomposition method and of the asymptotic decomposition method are considered for solution of nonlinear and/or stochastic partial differential equations in space and time Examples are given to show the potential for solving systems of equations even with strongly coupled boundary conditions

The diffusion-Brusselator equation

AbstractA solution is found for the reaction-diffusion equation, called the diffusion-Brusselator equation [1] using the decomposition method

On composite nonlinearities and the decomposition method

AbstractAccurate, convergent, computable solutions using the decomposition method have been demonstrated in and papers for wide classes of nonlinear and/or stochastic differential, partial differential, or algebraic equations. It is shown specifically in this paper that composite nonlinearities of the form Nx = N0(N1(N2(···(x)···) appearing in such equations where the Ni are nonlinear operators can also be handled with the Adomian An polynomials

Nonlinear transport in moving fluids

AbstractThe time-dependent spread of contaminants in moving fluids is normally studied by computer-intensive discretized procedures which have some disadvantages. Application of the decomposition method allows a continuous, convenient, accurate procedure which works and extends to nonlinear and stochastic partial differential equations as well

The Ginzburg-Landau equation

AbstractThe decomposition method is applied to the Ginzburg-Landau equation

An approach to steady-state solutions

AbstractThe steady-state solution of the nonlinear heat equation is calculated using the decomposition method

Stochastic contaminant transport equation in porous media

AbstractStochastic equations for the prediction of contaminant migration in porous media are considered by the use of the decomposition method. The results are easily generalized to the nonlinear case as well. Important applications of significance in the environmental sciences and engineering are beginning to appear in the literature, such as the forecasting of contaminant plume evolution in natural soils and aquifers after chemical spills, aquifer restoration, and groundwater pollution management

Studying nonlinear effects on the early stage of phase ordering using a decomposition method

Nonlinear effects on the early stage of phase ordering are studied using Adomian's decomposition method for the Ginzburg-Landau equation for a nonconserved order parameter. While the long-time regime and the linear behavior at short times of the theory are well understood, the onset of nonlinearities at short times and the breaking of the linear theory at different length scales are less understood. In the Adomian's decomposition method, the solution is systematically calculated in the form of a polynomial expansion for the order parameter, with a time dependence given as a series expansion. The method is very accurate for short times, which allows to incorporate the short-time dynamics of the nonlinear terms in a analytical and controllable way.Comment: 11 pages, 1 figure, to appear in Phys Lett