on a class of nonlinear dynamical systems the structure of a differential operator in the application of the decomposition method abstract a suitable expresion of a differential operator is deduced allowing the explicit calculation of the general term f h in the power series expansion of a function f x t to be utilized for solving nonlinear differential equations

polynomial nonlinearities in differential equations abstract adomian and his collaborators have found solutions for nonlinear stochastic or deterministic in the limiting case differential equations involving polynomial non linearities using the first author s a n polynomials and recently developed methods of calculating these polynomials it becomes very easy to write solutions for non linear terms such as y m for positive integers m the cases of negative integer m or even decimal powers will appear elsewhere

on the convergence region for decomposition solutions abstract the author s decomposition method using his a n polynomials for the nonlinearities has been shown to apply to wide classes of nonlinear or nonlinear stochastic operator equations providing a computable accurate solution which converges rapidly in computation the above is sufficient for a rapid test of convergence region

on the tricomi problem the tricomi equation is solved by the decomposition method 6 8 on the half space x y 0 and also for suitable boundary conditions given on the boundary of the hyperbolic elliptic domain

on the control of stochastic systems abstract a general model is available for analysis of control systems involving stochastic time varying parameters in the system to be controlled by the use of the iterative method of the authors or its more recent adaptations for stochastic operator equations it is shown that the statistical separability which is achieved as a result of the method for stochastic operator equations is unaffected by the matrix multiplications in state space equations the method therefore is applicable to the control problem application is made to the state space equation x ax bu c where a b c are stochastic matrices corresponding to stochastic operators i e involving randomly time varying elements e g a ij t a t t f a p s it is emphasized that the processes are arbitrary stochatic processes with known statistics no assumption is made of wiener or markov behavior or of smallness of fluctuations and no closure approximations are necessary the method differs in interesting aspects from volterra series expansions used by wiener and others and has advantages over the other methods because of recent progress in the solution of the nonlinear case it may be possible to generalize the results above to the nonlinear case as well but the linear case is suffcient to show the connections and essential point of separability of ensemble averages

new application of adomian decomposition method on fokker planck equation adomian decomposition method has been used for finding the explicit and numerical solutions of the reduced fokker planck equation in a force field the obtained results are compared with those found by other theories such as lie group theory the behaviour of the approximate distribution functions are shown graphically the results of lie group method confirm the correctness of those obtained by adomian decomposition method

convergent series solution of nonlinear equations abstract the author s decomposition method 1 provides a new efficient computational procedure for solving large classes of nonlinear and or stochastic equations these include differential equations containing polynomial exponential and trigonometric terms negative or irrational powers and product nonlinearities 2 also included are partial differential equations 3 delay differential equations 4 algebraic equations 5 and matrix equations 6 which describe physical systems essentially the method provides a systematic computational procedure for equations containing any nonlinear terms of physical significance the procedure depends on calculation of the author s a n a finite set of polynomials 1 13 in terms of which the nonlinearities can be expressed this paper shows important properties of the a n which ensure an accurate and computable convergent solution by the author s decomposition method 1 since the nonlinearities and or stochasticity which can be handled are quite general the results are potentially extremely useful for applications and make a number of common approximations such as linearization unnecessary

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

stability and resolution analysis for a topological derivative based imaging functional the aim of this paper is to study a topological derivative based anomaly detection algorithm we compare its performance with other imaging approaches such as multiple signal classification backpropagation and kirchhoff migration we also investigate its stability with respect to medium and measurement noises as well as its resolution a simple postprocessing of the data set is introduced and shown to be essential in order to obtain an efficient topological based imaging functional both in terms of resolution and stability

nonlinear plasma response abstract the decomposition method g adomian stochastic systems academic press new york london 1983 g adomian stochastic systems ii in press and earlier work of adomian referenced therein allows solution without linearization of problems normally requiring the self consistent field technique the latter technique can provide a sufficiently accurate approximation in weakly coupled plasma but the decomposition method of adomian provides a superior and physically preferable methodology for the general case

fisher and jaynesian statistics compared in the description of classical fluids fisher statistics provides an information measure which like that of shannon is a functional of a distribution f the latter solves an euler equation to minimize the functional to make comparison with statistical derivations of extended thermodynamics calculations by frieden plastino and collaborators are specialized to the case where f is a phase space distribution approximating a solution of the liouville equation the euler equations are solved subject to conditions specifying values of internal energy and fluxes e g of heat and momentum the solution is compared with that of jaynes which with information theory provides an entropy model the fisher and jaynes entropies are identical only in equilibrium the distributions agree in linear approximation for a restricted set of variables this set is large enough to embrace all those needed in the classical non equilibrium description of simple fluids fisher euler solutions are not unique in non equilibrium

fisher based thermodynamics its legendre transform and concavity properties it is shown that the legendre transform structure of thermodynamics can be replicated without any change if one replaces the entropy s by fisher s information measure i also the important thermodynamic property of concavity is shown to be obeyed by i by this use of the fisher information measure we develop a thermodynamics that seems to be able to treat equilibrium and nonequilibrium situations in a manner entirely similar to the conventional one

sharp error estimate of the nonuniform l1 formula for linear reaction subdiffusion equations stability and convergence of the l1 formula on nonuniform time grids are studied for solving linear reaction subdiffusion equations with the caputo derivative a discrete fractional gronwall inequality is developed for the nonuniform l1 formula by introducing a discrete convolution kernel of riemann liouville fractional integral to simplify the consistency analysis of the nonuniform l1 formula we bound the local truncation error in a discrete convolution form and consider a global convolution error involving the discrete riemann liouville integral kernel with the help of discrete fractional gronwall inequality and global consistency error analysis a sharp error estimate reflecting the regularity of solution is obtained for a simple l1 scheme numerical examples are provided to verify the sharpness of the error analysis

nonlinear differential equations with negative power nonlinearities abstract differential equations involving the term y m where m is a positive integer are solved by the decomposition method 1 3 441 452

solving nonlinear differential equations with decimal power nonlinearities abstract the decomposition method stochastic systems academic press new york 1983 nonlinear stochastic operator equations academic press new york in press is applied to the solution of nonlinear differential equations of the form ly ny x t where l is a linear differential operator and ny is a nonlinear term of the form y with a decimal number

stability for an inverse problem in potential theory let d be a subdomain of a bounded domain in r n the conductivity coefficient of d is a positive constant k 1 and the conductivity of d is equal to 1 for a given current density g on we compute the resulting potential u and denote by f the value of u on the general inverse problem is to estimate the location of d from the known measurements of the voltage f if d h is a family of domains for which the hausdorff distance d d d h equal to o h h small then the corresponding measurements f h are o h close to f

implicit explicit difference schemes for nonlinear fractional differential equations with nonsmooth solutions we propose second order implicit explicit imex time stepping schemes for nonlinear fractional differential equations with fractional order 0 beta 1 from the known structure of the nonsmooth solution and by introducing corresponding correction terms we can obtain uniformly second order accuracy from these schemes we prove the convergence and linear stability of the proposed schemes numerical examples illustrate the flexibility and efficiency of the imex schemes and show that they are effective for nonlinear and multirate fractional differential systems as well as multiterm fractional differential systems with nonsmooth solutions

recovery of high order accuracy in jacobi spectral collocation methods for fractional terminal value problems with non smooth solutions abstract an open problem in the numerical analysis of spectral methods for fractional differential equations is how to maintain the high order accuracy for non smooth solutions the limited regularity of the exact solution to these equations causes a deterioration in the orders of convergence of standard schemes in this paper we derive and analyze an exponentially accurate jacobi spectral collocation method for the numerical solution of nonlinear terminal value problems involving the caputo fractional derivative of rational order 0 1 the main ingredient of the proposed approach is to regularize the solution by a suitable smoothing transformation which allows us to adjust a parameter in the solution according to different given data to maximize the convergence rate we systematically describe the necessary steps in the implementation process additionally a comprehensive numerical analysis including error estimates under the l and weighted l 2 norms is derived the extensive numerical examples that accompany our analysis confirm our theoretical estimates as well as give additional insights into the convergence behavior of our method for problems with smooth and non smooth solutions

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

application of the decomposition method to inversion of matrices abstract the decomposition method g adomian stochastic systems academic press new york london 1983 is applied to inversion of matrices by approximation

a hybrid collocation method for volterra integral equations with weakly singular kernels the commonly used graded piecewise polynomial collocation method for weakly singular volterra integral equations may cause serious round off error problems due to its use of extremely nonuniform partitions and the sensitivity of such time dependent equations to round off errors the singularity preserving nonpolynomial collocation method is known to have only local convergence to overcome the shortcoming of these well known methods we introduce a hybrid collocation method for solving volterra integral equations of the second kind with weakly singular kernels in this hybrid method we combine a singularity preserving nonpolynomial collocation method used near the singular point of the derivative of the solution and a graded piecewise polynomial collocation method used for the rest of the domain we prove the optimal order of global convergence for this method the convergence analysis of this method is based on a singularity expansion of the exact solution of the equations we prove that the solutions of such equations can be decomposed into two parts with one part being a linear combination of some known singular functions which reflect the singularity of the solutions and the other part being a smooth function a numerical example is presented to demonstrate the effectiveness of the proposed method and to compare it to the graded collocation method

on uniqueness of recovery of a discontinuous conductivity coefficient on considere le probleme de retrouver le coefficient a de l equation elliptique div a u 0 dans un domaine avec la condition aux limites u sur quand u n est donnee pour tout regulier on demontre l unicite pour a a 0 b discontinu ou est la fonction indicateur d un ensemble ouvert a o est une fonction c 2 donnee et b est une fonction c 2 inconnue

error analysis of a finite difference method on graded meshes for a time fractional diffusion equation a reaction diffusion problem with a caputo time derivative of order alpha in 0 1 is considered the solution of such a problem is shown in general to have a weak singularity near the initial time t 0 and sharp pointwise bounds on certain derivatives of this solution are derived a new analysis of a standard finite difference method for the problem is given taking into account this initial singularity this analysis encompasses both uniform meshes and meshes that are graded in time and includes new stability and consistency bounds the final convergence result shows clearly how the regularity of the solution and the grading of the mesh affect the order of convergence of the difference scheme so one can choose an optimal mesh grading numerical results are presented that confirm the sharpness of the error analysis

second order numerical methods for multi term fractional differential equations smooth and non smooth solutions abstract starting with the asymptotic expansion of the error equation of the shifted grunwald letnikov formula we derive a new modified weighted shifted grunwald letnikov wsgl formula by introducing appropriate correction terms we then apply one special case of the modified wsgl formula to solve multi term fractional ordinary and partial differential equations and we prove the linear stability and second order convergence for both smooth and non smooth solutions when the regularity of the solutions is known we show theoretically and numerically that numerical solutions with good accuracy can be obtained with only a few correction terms moreover the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions numerical simulations verify the theoretical results and demonstrate that the new wsgl formula leads to better performance compared to other known numerical approximations with similar resolution

boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium we consider an isotropic lame system for an elastic medium consisting of finitely many imperfections of small diameter embedded in a homogeneous reference medium the lame coefficients of the imperfections are different from those of the background medium first we establish an asymptotic formula for the displacement vector in terms of the reference lame coefficients the location of the imperfections and their geometry second we use this asymptotic expansion to establish continuous dependence estimates for certain characteristics of the imperfections in terms of the boundary data and to derive integral boundary formulae that yield to a very effective identification procedure

optimization algorithm for reconstructing interface changes of a conductivity inclusion from modal measurements we propose an original optimization approach for reconstructing interface changes of a conductivity inclusion from measurements of eigenvalues and eigenvectors associated with the transmission problem for the laplacian let be a smooth domain and d be an inclusion contained in whose boundary is also assumed to be smooth shape deformation of d causes a perturbation of modal parameters the aim of this work is to show how this information can be used to reconstruct the unknown deformation for doing so we rigorously derive an asymptotic formula for the perturbations in the eigenvalues of the transmission problem for the laplacian that are due to small deformations of the interface of an inclusion based on this formula we design an efficient reconstruction algorithm from modal measurements our algorithm consists on minimizing a functional whose minimizer yields certain geometric properties of the unknown inclusion it naturally follows from a key identity that is in some sense dual to the asymptotic formula numerical experiments showing the viability of our algorithm are presented our results in this paper extend those established in the context of small volume inclusions as well as those for the conductivity interface problem in fact on one hand in a series of recent papers 5 3 1 2 we have derived high order asymptotic expansions of the eigenvalue perturbations due to the presence of small inclusions and used them for locating the inclusions and identifying some of their geometric features on the other hand in 4 we have derived highorder terms in the asymptotic expansions of the boundary perturbations of steady state voltage potentials resulting from small perturbations of the shape of a conductivity inclusion based on these derivations we have designed an effective algorithm to determine some geometric features of the shape perturbation of the inclusion based on boundary measurements

imaging schemes for perfectly conducting cracks we consider the problem of locating perfectly conducting cracks and estimating their geometric features from multistatic response matrix measurements at a single or multiple frequencies a main objective is to design specific crack detection rules and to analyze their receiver operating characteristics and the associated signal to noise ratios in this paper we introduce an analytic framework that uses asymptotic expansions which are uniform with respect to the wavelength to crack size ratio in combination with a hypothesis test based formulation to construct specific procedures for detection of perfectly conducting cracks a central ingredient in our approach is the use of random matrix theory to characterize the signal space associated with the multistatic response matrix measurements we present numerical experiments to illustrate some of our main findings

topological and shape gradient strategy for solving geometrical inverse problems abstract in this paper we present a technique for shape reconstruction based on the topological and shape gradients the shape in consideration is a solution of an inverse conductivity problem to solve such a problem numerically we compute the topological gradient of a kohn vogelius type cost function when the domain under consideration is perturbed by the introduction of a small inclusion instead of a hole the reconstruction is done by considering the shape as a superposition of very thin elliptic inclusions to get a first approximation then we use a gradient type algorithm to perform a good reconstruction various numerical experiments of single and multiple inclusions demonstrate the viability of the designed algorithm

algebraic equations with exponential terms abstract the decomposition method is applied to algebraic equations containing exponential terms the n term approximation n is rapidly damped as n increases yielding an oscillating convergence of superior accuracy n 5 and n 9 for k 2

adomian s decomposition method for solving an intermediate fractional advection dispersion equation this paper is concerned with a model that describes the intermediate process between advection and dispersion via fractional derivative in the caputo sense adomian s decomposition method is used for solving this model the solution is obtained as an infinite series which always converges to the exact solution

analysis of a time stepping scheme for time fractional diffusion problems with nonsmooth data this paper establishes the convergence of a time stepping scheme for the time fractional diffusion problems with nonsmooth data we first analyze the regularity of the time fractional diffusion pro

transient behaviour of semilinear stochastic systems with random parameters abstract the transient solution of a class of nonautonomous stochastic differential equations with given random initial conditions is studied the considered evolution equation is characterized by the presence of a deterministic linear term and of a random nonlinear term whose parameters can be modeled by random processes of rice noise type analytical approximated expressions for the first and second order moments and for the probability density of the solution process are derived and are applied to determine the statistical properties of a class of stochastic nonlinear oscillators

on composite nonlinearities and the decomposition method abstract accurate 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

on green s function in higher order stochastic differential equations abstract in adomian s solution of linear or nonlinear deterministic or stochastic differential equations the decomposition of the linear part into l r can be made so as to simplify green s function and consequently the resulting computations

on the solutions of stochastic initial value problems in continuum mechanics abstract this work deals with the analysis of a class of initial value problems for nonlinear hyperbolic equations with stochastic process coefficients and four time space independent variables a perturbation procedure is developed leading to a sequence of stochastic partial differential equations which are solved by application of the adomian decomposition method a pertinent application in mechanics is also considered and quantitative results are presented and discussed

schrodinger equation from an exact uncertainty principle an exact uncertainty principle formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position leads from the classical equations of motion to the schrodinger equation

the topological asymptotic expansion for the dirichlet problem the topological sensitivity analysis provides an asymptotic expansion of a shape function when creating a small hole inside a domain this expansion yields a descent direction which can be used for shape optimization if one wishes to keep a classical domain throughout the optimization process in this paper such an expansion is obtained for the poisson equation for a large class of cost functions and arbitrarily shaped holes in the three dimensional case this expansion depends on the shape of the hole but not on its orientation if the cost function involves only the solution u to the underlying partial differential equation whereas it may also depend on its orientation if the cost function involves the gradient nabla u in contrast the asymptotic expansion is independent of the shape in the two dimensional case a numerical example illustrates the use of the asymptotic expansion which yields a minimizing sequence of classical domains in a case where no classical solution exists

topological sensitivity analysis the so called topological derivative concept has been seen as a powerful framework to obtain the optimal topology for several engineering problems this derivative characterizes the sensitivity of the problem when a small hole is created at each point of the domain however the greatest limitation of this methodology is that when a hole is created it is impossible to build a homeomorphic map between the domains in study because they have not the same topology therefore some specific mathematical framework should be developed in order to obtain the derivatives this work proposes an alternative way to compute the topological derivative based on the shape sensitivity analysis concepts the main feature of this methodology is that all the mathematical procedure already developed in the context of shape sensitivity analysis may be used in the calculus of the topological derivative this idea leads to a more simple and constructive formulation than the ones found in the literature further to point out the straightforward use of the proposed methodology it is applied for solving some design problems in steady state heat conduction

on a class of nonlinear stochastic dynamical systems analysis of the transient behaviour abstract a class of nonlinear dynamical systems with random parameters and initial conditions is considered the transient time evolution of the mean value of the dependent variable is analyzed both by means of the stochastic averaging method and by adomian s decomposition method a proof of the equivalence of the decomposition method to the time series approximation of the dynamical response is provided an application is made to the van der pol equation and finally a comparison between the two previously discussed methods is given

stochastic model for colored noise abstract the input output point of view for the ito equation to avoid stochastic integration is related to the stochastic operator approach for a physically reasonable robust mathematical model

an application of the decomposition method to the matrix riccati equation in a neutron transport process abstract the differential matrix riccati equation with matrix variable coefficients arising in transport theory is considered an analytical approximation of the solution of the non linear equation is investigated using the adomian decomposition method and an application to neutron steady state process is proposed to test the accuracy of the method

on adomian s decomposition method and some comparisons with picard s iterative scheme abstract we consider the general mathematical framework of adomian s decomposition method g adomian stochastic systems academic press new york 1983 for a large class of nonlinear operator equations picard s iterative scheme is considered for the same class for equations and compared with the decomposition method the paper identifies carefully all substantial differences between the two methods and shows that various advantages exist for the decomposition method

non extensive statistical mechanics and generalized fokker planck equation a non linear generalized fokker planck gfp equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by tsallis in his generalization of statistical mechanics in the case of a constant or linearly varying drift the time dependent solutions of the gfp equation are seen to obey a suitable form of the celebrated h theorem the temporal changes of tsallis entropies are seen to be given in terms of the fisher s information measure particular time dependent solutions of the gfp equation of the maximum tsallis entropy form are obtained

topological sensitivity and shape optimization for the stokes equations the topological sensitivity analysis provides an asymptotic expansion of a shape function with respect to the insertion of a small hole or obstacle inside a domain this expansion can then be used for shape optimization in this paper such an expansion is obtained for the stokes equations with general shape functions and arbitrarily shaped holes a numerical example illustrates the use of the topological sensitivity in a shape optimization problem

conductivity interface problems part i small perturbations of an interface we derive high order terms in the asymptotic expansions of boundary perturbations of steady state voltage potentials resulting from small perturbations of the shape of a conductivity inclusion with c 2 boundary our derivation is rigorous and based on layer potential techniques the asymptotic expansion in this paper is valid for c 1 perturbations and inclusions with extreme conductivities it extends those already derived for small volume conductivity inclusions and leads us to very effective algorithms for determining lower order fourier coefficients of the shape perturbation of the inclusion based on boundary measurements we perform some numerical experiments using the algorithm to test its effectiveness

a convenient computational form for the adomian polynomials abstract recent important generalizations by g adomian stochastic systems academic press 1983 have extended the scope of his decomposition method for nonlinear stochastic operator equations see also iterative method inverse operator method symmetrized method or stochastic green s function method very considerably so that they are now applicable to differential partial differential delay and coupled equations which may be strongly nonlinear and or strongly stochastic or linear or deterministic as subcases thus for equations modeling physical problems solutions are obtained rapidly easily and accurately the methodology involves an analytic parametrization in which certain polynomials an dependent on the nonlinearity are derived this paper establishes simple symmetry rules which yield adomian s polynomials quickly to high orders

a comparison between adomian s decomposition methods and perturbation techniques for nonlinear random differential equations abstract comparison of the adomian decomposition method and regular perturbation techniques applied to the solution of nonlinear vector random differential equations shows that the decomposition method is superior and generally applicable even for the cases where perturbation is applicable the comparison shows that the decomposition method is easier to compute and supplies quantitatively reliable results

weakly non local fluid mechanics the schrodinger equation a weakly non local extension of ideal fluid dynamics is derived from the second law of thermodynamics it is proved that in the reversible limit the additional pressure term can be derived from a potential the requirement of the additivity of the specific entropy function determines the quantum potential uniquely the relation to other known derivations of the schrodinger equation stochastic fisher information exact uncertainty is clarified

nonlinear stochastic differential delay equations abstract the methods used by adomian and his co workers to solve linear and nonlinear stochastic differential equations will be demonstrated to be applicable to differential equations deterministic or stochastic involving delays constant time dependent or random

a finite difference scheme on graded meshes for time fractional nonlinear korteweg de vries equation abstract in this paper a finite difference scheme for time fractional nonlinear korteweg de vries kdv problems with the caputo type fractional derivative is presented to deal with the weak singularity caused by the fractional derivative that the solution has in the initial layer the well known l1 scheme on graded meshes has been used for time discretization meanwhile a nonlinear finite difference approximation on uniform meshes is proposed for spatial discretization the existence stability and convergence of the numerical solution are studied by the energy method it is proved that the scheme is of min 2 r order convergence in time and of first order convergence in space where is the order of fractional derivative and r is a parameter of graded meshes furthermore in order to increase computational efficiency the corresponding fast algorithm of the presented scheme has been considered in numerical simulation a valid approach based on linear interpolation is designed to test convergence rate for the scheme on temporal graded meshes numerical results demonstrate sharpness of the theoretical convergence estimate and effectiveness of the fast algorithm

semilinear stochastic systems analysis with the method of the stochastic green s function and application in mechanics abstract this work deals with the analysis of a class of semilinear vector stochastic operator equations the method of the stochastic green s function due to adomian is extended to the above mentioned class of equations some perturbation techniques are also developed and a pertinent application in nonlinear mechanics is considered

shape sensitivity analysis for an interface problem via minimax differentiability this paper deals with the shape sensitivity analysis for the conductivity problem with discontinuous coefficients we consider the geometric inverse problem of locating the interfaces where the jump of the coefficients occurs we propose a reconstruction method based on the minimization of the kohn vogelius functional the reformulation of the functional in a suitable saddle point problem form allows us to obtain the optimality conditions by using the differentiability of the minimax combined with the function space parametrization technique an important advantage of this approach is that it avoids the differentiability of the state variable with respect to the domain the reconstruction is then performed with an iterative algorithm using an appropriate quasi newton method we give some numerical examples showing the efficiency of the method

coupled differential equations and coupled boundary conditions abstract it is demonstrated that the high accuracy for approximations requiring only a few terms which is typical of the decomposition method for nonlinear stochastic operator equations or special cases linear or deterministic holds for coupled equations and coupled boundary conditions as well

an inverse initial boundary value problem for the wave equation in the presence of imperfections of small volume we consider for the wave equation the inverse problem of identifying locations and certain properties of the shapes of small conductivity inhomogeneities in a homogeneous background medium from dynamic boundary measurements on part of the boundary and for a finite interval in time using as weights particular background solutions constructed by a geometrical control method we develop an asymptotic method based on appropriate averaging of the partial dynamic boundary measurements our approach is expected to lead to very effective computational identification algorithms

numerical comparison of methods for solving a special fourth order boundary value problem in this paper we implement relatively new analytical techniques the differential transform method adomian decomposition and homotopy perturbation method for solving a fourth order boundary value problem in these schemes the solution takes the form of a convergent series with easily computable components this paper will present a numerical comparison between the three methods for solving a fourth order boundary value problem the numerical results demonstrates that the new methods are quite accurate and efficient for this kind of problems

coupled nonlinear stochastic differential equations abstract systems of n coupled linear or nonlinear differential equations which may be deterministic or stochastic are solved by methods of the first author and his co workers examples include two coupled riccati equations coupled linear equations stochastic coupled equations with product terms and n coupled stochastic differential equations

a study on compacton like solutions for the modified kdv and fifth order kdv like equations in this work we study compacton like solutions for the modified kdv and fifth order kdv like equations we present compacton like solutions of the integrable nonlinear equations although the behavior of the obtained solution is reminiscent of the solitons yet its second derivative is discontinuous at the boundaries a feature characterizing the compactons

unique additive information measures boltzmann gibbs shannon fisher and beyond abstract it is proved that the only additive and isotropic information measure that can depend on the probability distribution and also on its first derivative is a linear combination of the boltzmann gibbs shannon and fisher information measures power law equilibrium distributions are found as a result of the interaction of the two terms the case of second order derivative dependence is investigated and a corresponding additive information measure is given

nonlinear stochastic dynamical systems in physical problems abstract a number of important equations of physics are shown to fit into the structure of a nonlinear stochastic differential equation which can then be solved by the decomposition method