the variational iteration method for solving two forms of blasius equation on a half infinite domain the variational iteration method is applied for a reliable treatment of two forms of the third order nonlinear blasius equation which comes from boundary layer equations the study shows that the series solution is obtained without restrictions on the nonlinearity behavior the obtained series solution is combined with the diagonal pade approximants to handle the boundary condition at infinity for only one of these forms

reconstruction from image sequences by means of relative depths this paper deals with the problem of reconstructing the locations ofn points in space from m different images without camera calibration it shows how these problems can be put into a similar theoretical framework a new concept the reduced fundamental matrix is introduced it contains just 4 parameters and can be used to predict locations of points in the images and to make reconstruction we also introduce the concept of reduced fundamental tensor which describes the relations between points in 3 images it has 15 components and depends on 9 parameters necessary and sufficient conditions for a tensor to be a reduced fundamental tensor are derived this framework can be generalised to a sequence of images the dependencies between the different representations are investigated furthermore a canonical form of the camera matrices in a sequence are presented

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

machine learning and nonparametric bandit theory in its most basic form bandit theory is concerned with the design problem of sequentially choosing members from a given collection of random variables so that the regret i e r sub n spl sigma sub j spl mu spl mu sub j et sub n j grows as slowly as possible with increasing n here spl mu sub j is the expected value of the bandit arm i e random variable indexed by j t sub n j is the number of times arm j has been selected in the first n decision stages and spl mu sup sup sub j spl mu sub j the present paper contributes to the theory by considering the situation in which observations are dependent to begin with the dependency is presumed to depend only on past observations of the same arm but later we allow that it may be with respect to the entire past and that the set of arms is infinite this brings queues and more generally controlled markov processes into our purview thus our black box methodology is suitable for the case when the only observables are cost values and in particular the probability structure and loss function are unknown to the designer the conclusion of the analysis is that under lenient conditions using algorithms prescribed herein risk growth is commensurate with that in the simplest i i d cases our methods represent an alternative to stochastic approximation perturbation analysis ideas for tuning queues

super cubic iterative methods to solve systems of nonlinear equations two super cubic convergence methods to solve systems of nonlinear equations are presented the first method is based on the adomian decomposition method we state and prove a theorem which shows the cubic convergence for this method but numerical examples show super cubic convergence the second method is based on a quadrature formulae to obtain the inverse of jacobian matrix numerical examples show high order convergence for both methods

on the convergence of he s variational iteration method in this work we will consider he s variational iteration method for solving second order initial value problems we will discuss the use of this approach for solving several important partial differential equations this method is based on the use of lagrange multipliers for identification of optimal value of a parameter in a functional this procedure is a powerful tool for solving the large amount of problems using the variational iteration method it is possible to find the exact solution or an approximate solution of the problem this technique provides a sequence of functions which converges to the exact solution of the problem our emphasis will be on the convergence of the variational iteration method in the current paper this scheme will be investigated in details and efficiency of the approach will be shown by applying the procedure on several interesting and important models

a new analytic algorithm of lane emden type equations an reliable ease to use analytic algorithm is provided for lane emden type equation which models many phenomena in mathematical physics and astrophysics this algorithm logically contains the well known adomian decomposition method different from all other analytic techniques this algorithm itself provides us with a convenient way to adjust convergence regions even without pade technique some applications are given to show its validity

piecewise homotopy methods for nonlinear ordinary differential equations abstract piecewise homotopy perturbation methods are developed for the solution of nonlinear ordinary differential equations these methods are based on the introduction of an artificial or book keeping parameter and the expansion of the solution in a power series of this parameter and provide analytical solutions in open intervals which are smooth everywhere three piecewise adaptive homotopy perturbation methods based on the use of either a fixed number of approximants and a variable step size a variable number of approximants and a fixed step size or a variable number of approximants and a variable step size are presented and applied to eight nonlinear ordinary differential equations it is shown that piecewise adaptive homotopy perturbation methods predict essentially the same solutions as matlab s variable step variable order solvers and variable order transition matrix techniques provided that five term approximations of the decomposition method are applied to both the displacement and the velocity it is also shown that piecewise homotopy perturbation techniques that use three term approximations to both the displacement and the velocity provide essentially the same results as those obtained with a second order accurate time linearization technique when the same step is employed in both schemes

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

harmonic wave generation in non linear thermoelasticity by variational iteration method and adomian s method this paper applies the variational iteration method and adomian s decomposition method to solve numerically the harmonic wave generation in a nonlinear one dimensional elastic half space model subjected initially to a prescribed harmonic displacement the results show that the variational iteration method is much easier more convenient and more stable and efficient than adomian decomposition method

on the order of convergence of adomian method in this paper we contemplate the order of convergence of the decomposition method and we apply the results to some problems

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

adomian decomposition method for a reliable treatment of the bratu type equations in this paper we present a framework to determine exact solutions of bratu type equations the algorithm rests mainly on the adomian decomposition method the proposed scheme is illustrated by studying two boundary value problems and an initial value problem of bratu type the first type gives a solution that blows up at the middle of the domain whereas the other equations give bounded solutions

active learning in heteroscedastic noise we consider the problem of actively learning the mean values of distributions associated with a finite number of options the decision maker can select which option to generate the next observation from the goal being to produce estimates with equally good precision for all the options if sample means are used to estimate the unknown values then the optimal solution assuming that the distributions are known up to a shift is to sample from each distribution proportional to its variance no information other than the distributions variances is needed to calculate the optimal solution in this paper we propose an incremental algorithm that asymptotically achieves the same loss as an optimal rule we prove that the excess loss suffered by this algorithm apart from logarithmic factors scales as n 3 2 which we conjecture to be the optimal rate the performance of the algorithm is illustrated on a simple problem

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

the variational iteration method for rational solutions for kdv k 2 2 burgers and cubic boussinesq equations in this work the reliable variational iteration method is used to determine rational solutions for the kdv the k 2 2 the burgers and the cubic boussinesq equations the study highlights the efficiency of the method and its dependence on the lagrange multiplier rational solutions are obtained directly in a straightforward manner

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

modal hermite spectral collocation method for solving multi dimensional hyperbolic telegraph equations abstract the present research is contemplated proposing a numerical solution of multi dimensional hyperbolic telegraph equations with appropriate initial time and boundary space conditions the truncated hermite series with unknown coefficients are used for approximating the solution in both of the spatial and temporal variables the basic idea for discretizing the considered one dimensional 1d two dimensional 2d and three dimensional 3d telegraph equations is based on the collocation method together with the hermite operational matrices of derivatives the resulted systems of linear algebraic equations are solved by some efficient methods such as lu factorization the solution of the algebraic system contains the coefficients of the truncated hermite series numerical experiments are provided to illustrate the accuracy and efficiency of the presented numerical scheme comparisons of numerical results associated to the proposed method with some of the existing numerical methods confirm that the method is accurate and fast experimentally

homotopy perturbation method for solving hyperbolic partial differential equations this paper applies the homotopy perturbation method proposed by ji huan he to obtain approximate analytic solutions of hyperbolic partial differential equations the procedure of the method is systematically illustrated to give an extensive account of the method some examples are provided the results derived by this method will be compared with the results of characteristics method the results of homotopy perturbation method are of high accuracy verifying that the method is very effective and promising

a new iterative method to compute nonlinear equations the aim of this paper is to construct a new efficient iterative method to solve nonlinear equations the new method is based on the proposals of abbasbandy on improving the order of accuracy of newton raphson method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method applied mathematics and computation 145 2003 887 893 and on the proposals of babolian and biazar on improving the order of accuracy of adomian s decomposition method e babolian j biazar on the order of convergence of adomian method applied mathematics and computation 130 2002 383 387 the convergence of the new scheme is proved and at least the cubic order of convergence is established several examples are presented and compared to other methods showing the accuracy and fast convergence of this new method also it is shown in this paper that the modified adomian s method developed by babolian and biazar to solve nonlinear equations e babolian j biazar solution of nonlinear equations by modified adomian decomposition method applied mathematics and computation 132 2002 167 172 should be slightly modified due to the fact that convergence of adomian s method does not ensure convergence of the modified method an example illustrates this fact which unlike what is claimed by the authors does not converge with their method but with a simple different choice of the zero component becomes convergent

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

adomian decomposition method for burger s huxley and burger s fisher equations the approximate solutions for the burger s huxley and burger s fisher equations are obtained by using the adomian decomposition method solving frontier problems of physics the decomposition method kluwer boston 1994 the algorithm is illustrated by studying an initial value problem the obtained results are presented and only few terms of the expansion are required to obtain the approximate solution which is found to be accurate and efficient

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

exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method the purpose of this study is to introduce a modification of the homotopy perturbation method using laplace transform and pade approximation to obtain closed form solutions of nonlinear coupled systems of partial differential equations two test examples are given the coupled nonlinear system of burger equations and the coupled nonlinear system in one dimensional thermoelasticity the results obtained ensure that this modification is capable of solving a large number of nonlinear differential equations that have wide application in physics and engineering

invariants of six points and projective reconstruction from three uncalibrated images there are three projective invariants of a set of six points in general position in space it is well known that these invariants cannot be recovered from one image however an invariant relationship does exist between space invariants and image invariants this invariant relationship is first derived for a single image then this invariant relationship is used to derive the space invariants when multiple images are available this paper establishes that the minimum number of images for computing these invariants is three and the computation of invariants of six points from three images can have as many as three solutions algorithms are presented for computing these invariants in closed form the accuracy and stability with respect to image noise selection of the triplets of images and distance between viewing positions are studied both through real and simulated images applications of these invariants are also presented both the results of faugeras 1992 and hartley et al 1992 for projective reconstruction and sturm s method 1869 for epipolar geometry determination from two uncalibrated images with at least seven points are extended to the case of three uncalibrated images with only six points

experimentation with two step adomian decomposition method to solve evolution models the two step adomian decomposition method tsadm is derived by separate the standard adomian decomposition method into two steps although the tsadm needs only a slight variation from the standard adomian decomposition method experimentation shows that the tsadm is also promising for systems of inhomogeneous differential and integral equations hyperbolic partial differential equations and singular initial value problems

an approximation to the solution of hyperbolic equations by adomian decomposition method and comparison with characteristics method adomian decomposition method has been applied to solve many functional equations so far in this work this method is applied to solve hyperbolic partial differential equations and results will be compared with characteristics method

he s variational iteration method for fourth order parabolic equations he s variational iteration method is applied to fourth order parabolic partial differential equations with variable coefficients to illustrate the ability and reliability of the method some examples are given revealing its effectiveness and simplicity

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

on the convergence of adomian decomposition method here a simple method to determine the rate of convergence of adomian decomposition method is introduced the proposed method is used to compare between the rate of convergence of standard and modified proposed by wazwaz a m wazwaz a new method for solving singular initial value problems in the second order ordinary differential equations appl math comput 128 2002 45 57 adomian methods for solving lane emden singular problem furthermore with providing some examples the aforementioned cases are dealt with numerically

numerical solution of differential equations in the deterministic limit of stochastic theory although the methodology of stochastic differential equations was developed to achieve statistical separability in the stochastic case the deterministic limit is investigated both as a verification of the theory and also for possible value as a deterministic technique

a numerical solution of second order linear partial differential equations by differential transform two dimensional differential transform provides an effective tool to numerically solve partial differential equations in this paper we propose a general numerical solution of second order linear partial differential equations using two dimensional differential transform numerical examples justify the proposed scheme

adaptive strategy for stratified monte carlo sampling we consider the problem of stratified sampling for monte carlo integration of a random variable we model this problem in a k armed bandit where the arms represent the k strata the goal is to estimate the integral mean that is a weighted average of the mean values of the arms the learner is allowed to sample the variable n times but it can decide on line which stratum to sample next we propose an ucb type strategy that samples the arms according to an upper bound on their estimated standard deviations we compare its performance to an ideal sample allocation that knows the standard deviations of the arms for sub gaussian arm distributions we provide bounds on the total regret a distribution dependent bound of order poly min 1 o n 3 2 1 that depends on a measure of the disparity min of the per stratum variances and a distribution free bound poly k o n 7 6 that does not we give similar but somewhat sharper bounds on a proxy of the regret the problem independent bound for this proxy matches its recent minimax lower bound in terms of n up to a log n factor

contrasts in the basins of attraction of structurally identical iterative root finding methods a numerical comparison is performed between three methods of third order with the same structure namely bsc halley s and euler chebyshev s methods as the behavior of an iterative method applied to a nonlinear equation can be highly sensitive to the starting points the numerical comparison is carried out allowing for complex starting points and for complex roots on the basins of attraction in the complex plane several examples of algebraic and transcendental equations are presented

solution of systems of integral differential equations by adomian decomposition method in this article adomian decomposition method as a well known method for solving functional equations has been employed to solve systems of integral differential equations theoretical considerations are discussed and convergence of the method for these systems is addressed some examples are presented to show the ability of the method for such systems

solution of wave equation by adomian decomposition method and the restrictions of the method adomian decomposition has been applied to solve many functional equations so far in this article we have used this method to solve the wave equation which governs numerous engineering experimentations particularly in geoscience applications some special cases of the equation are solved as examples to illustrate the reliableness of the method restrictions on using adomian decomposition method for these equations are discussed

in defense of the eight point algorithm the fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras and the eight point algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches it has the advantage of simplicity of implementation the prevailing view is however that it is extremely susceptible to noise and hence virtually useless for most purposes this paper challenges that view by showing that by preceding the algorithm with a very simple normalization translation and scaling of the coordinates of the matched points results are obtained comparable with the best iterative algorithms this improved performance is justified by theory and verified by extensive experiments on real images

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

on the solution of algebraic equations by the decomposition method abstract the decomposition method g adomian stochastic systems academic press new york 1983 developed to solve nonlinear stochastic differential equations has recently been generalized to nonlinear and or stochastic partial differential equations systems of equations and delay equations and applied to diverse applications as pointed out previously see reference above the methodology is an operator method which can be used for nondifferential operators as well extension has also been made to algebraic equations involving real or complex coefficients this paper deals specifically with quadratic cubic and general higher order polynomial equations and negative or nonintegral powers and random algebraic equations further work on this general subject appears elsewhere g adomian stochastic systems ii academic press new york in press

a comparison between the variational iteration method and adomian decomposition method in this paper we present a comparative study between the variational iteration method and adomian decomposition method the study outlines the significant features of the two methods the analysis will be illustrated by investigating the homogeneous and the nonhomogeneous advection problems

an alternate algorithm for computing adomian polynomials in special cases in this article we introduce an alternate algorithm for computing adomian polynomials and present some examples to show the simplicity and efficiency of the new method

an artificial parameter decomposition method for nonlinear oscillators applications to oscillators with odd nonlinearities abstract a method for obtaining series solutions of nonlinear second order ordinary differential equations based on the introduction of an artificial parameter is presented and shown to be identical to the well known adomian s decomposition technique the method is formulated in both integral and differential forms for the determination of the limit cycle of oscillators with odd nonlinearities two differential forms and one integral form of the artificial parameter method are presented these versions are based on introducing a linear stiffness term with an unknown frequency and the use of either the original independent variable or a new independent variable that depends linearly on the unknown frequency of the oscillator the three formulations provide identical results and their application to eight oscillators with odd nonlinearities shows that the artificial parameter technique presented in this paper predicts the same frequency of oscillation as the harmonic balance and iterative techniques as well as modified linstedt poincare methods however the method presented here is based on the introduction of an artificial parameter and does not require the presence of small perturbation parameters in the ordinary differential equation it is also shown that two and three level iterative methods yield the same frequency of oscillation as the artificial parameter technique presented in this paper provided that the initial iterate of the former coincides with the leading order solution of the latter and only one iteration of iterative techniques and only the second approximation of the artificial parameter method are determined

the key to three view geometry in this article we describe a set of canonical transformations of the image spaces that make the description of three view geometry very simple the transformations depend on the three view geometry and the canonically transformed trifocal tensor mathcal t takes the form of a sparse array where 17 elements in well defined positions are zero it has a linear relation to the camera matrices and to two of the fundamental matrices a third order relation to the third fundamental matrix a second order relation to the other two trifocal tensors and first order relations to the 10 three view all point matching constraints in this canonical form it is also simple to determine if the corresponding camera configuration is degenerate or co linear an important property of the three canonical transformations of the images spaces is that they are in so 3 the 9 parameters needed to determine these transformations and the 9 parameters that determine the elements of mathcal t together provide a minimal parameterization of the tensor it does not have problems with multiple maps or multiple solutions that other parameterizations have and is therefore simple to use it also provides an implicit representation of the trifocal internal constraints the sparse canonical representation of the trifocal tensor can be determined if and only if it is consistent with its internal constraints in the non ideal case the canonical transformation can be determined by solving a minimization problem and a simple algorithm for determining the solution is provided this allows us to extend the standard linear method for estimation of the trifocal tensor to include a constraint enforcement as a final step similar to the constraint enforcement of the fundamental matrix experimental evaluation of this extended linear estimation method shows that it significantly reduces the geometric error of the resulting tensor but on average the algebraic estimation method is even better for a small percentage of cases however the extended linear method gives a smaller geometric error implying that it can be used as a complement to the algebraic method for these cases

algebraic functions for recognition in the general case a trilinear relationship between three perspective views is shown to exist the trilinearity result is shown to be of much practical use in visual recognition by alignment yielding a direct reprojection method that cuts through the computations of camera transformation scene structure and epipolar geometry moreover the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection the proof of the central result may be of further interest as it demonstrates certain regularities across homographics of the plane and introduces new view invariants experiments on simulated and real image data were conducted including a comparative analysis with epipolar intersection and the linear combination methods with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks

solution of the fully fuzzy linear systems using the decomposition procedure abstract this paper tries to extend the adomian decomposition method for solving fully fuzzy linear systems shown as ffls for finding a positive fuzzy vector x that satisfies a x b where a and b are respectively a fuzzy matrix and a fuzzy vector we employ dubois and prade s approximate arithmetic operators on lr fuzzy numbers we also transform the ffls and use the adomian decomposition method for solving an ffls then we compare this method with the jacobi iterative technique additionally we give some numerical examples

a new bernoulli matrix method for solving second order linear partial differential equations with the convergence analysis in this paper a new matrix approach for solving second order linear partial differential equations pdes under given initial conditions has been proposed the basic idea includes integrating from the considered pdes and transforming them to the associated integro differential equations with partial derivatives therefore bernoulli operational matrices of differentiation and integration together with the completeness of bernoulli polynomials can be used for transforming integro differential equations to the corresponding algebraic equations a rigorous error analysis in the infinity norm is given provided that the known functions and the exact solution are sufficiently smooth and bounded a numerical example is included to demonstrate the validity and the applicability of the technique the results confirm the theoretical prediction

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

comparing numerical methods for the solutions of two dimensional diffusion with an integral condition in this paper we present a numerical comparison between the adomian decomposition method adm and a fourth order explicit finite difference method for solving two dimensional diffusion problems with an integral condition the numerical results show that the adm is quite accurate and easily implemented

comments on the basto semiao calheiros root finding method abstract in the recent paper m basto v semiao f l calheiros a new iterative method to compute nonlinear equations appl math comput 173 2006 468 483 a new cubically convergent iterative method for solving nonlinear equations was proposed in this paper we give some comments that point to significant similarity of the proposed method to the classic euler chebyshev method and discuss the efficiency of the new method in a comparison procedure involving five other third order methods with similar structure five numerical examples four of them used in the cited paper showed that the convergence behavior of the new method is equal or worse than competitive tested methods some comments on iterative methods involving the third derivative are also exposed

an extension of the decomposition method for solving nonlinear equations and its convergence in this paper we propose an extension of the decomposition method for solving nonlinear equations after a summary of adomian s decomposition method adm a new kind of decomposition strategy for nonlinear functions in nonlinear equations is proposed and a generalized decomposition method gdm for solving nonlinear equations is presented under a rather mild condition the convergence of the gdm is proved also some concrete examples are studied to illustrate with numerical results how powerful the gdm is finally some general remarks conclude this study

a modified spectral method for solving operator equations in this paper we introduce a modified spectral method for solving the linear operator equation l u f l d l h 1 h 2 where h 1 and h 2 are normed vector spaces with norms 1 and respectively and d l is the domain of l also for each h h 2 h 2 h h where is an inner product on h 2 in this method we make a new set n n 0 for h 1 using l and two sets in h 1 and h 2 then using the new set n n 0 we solve this linear operator equation we show that this method does not have some shortcomings of spectral method also we prove the stability and convergence of the new method after introducing the method we give some conditions that under them the nonlinear operator equation l u n u f can be solved some examples are considered to show the efficiency of method

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 new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

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

a new iterative method for solving nonlinear equations abstract in this paper we present a new efficient iterative method for solving nonlinear equations improving newton raphson method this method is based on a modification of the proposal of abbasbandy on improving the order of accuracy of newton raphson method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method appl math comput 145 2003 887 893 the convergence properties of the method and some other methods are discussed some numerical illustrations are given to show that the proposed method behaves equal or better performance compared to the other methods of same kind

an improvement to the fixed point iterative method the problem of convergence of the fixed point iterative method has been studied in this article the main object of this article is to improve the convergence so that the number of iterations is reduced to just few iterations a technique is presented to increase the order of convergence as much as desired to illustrate the ability of this technique some examples for which regular method needs many times of iterations are presented

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

solution of nonlinear equations by modified adomian decomposition method in this paper we modify the standard adomian method for solution of the nonlinear equation f x 0 four examples are presented and compared using standard and modified adomian methods

extracting a general iterative method from an adomian decomposition method and comparing it to the variational iteration method in this work a new form of adomian decomposition method adm is presented by this form a general iterative method can be achieved in which there is no need of calculating adomian polynomials also this general iterative method is compared with the adomian decomposition method and variational iteration method vim and its advantages are expressed

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

homotopy perturbation transform method for nonlinear equations using he s polynomials in this paper a combined form of the laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations this method is called the homotopy perturbation transform method hptm the nonlinear terms can be easily handled by the use of he s polynomials the proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round off errors the fact that the proposed technique solves nonlinear problems without using adomian s polynomials can be considered as a clear advantage of this algorithm over the decomposition method