on a family of iterative methods for simultaneous extraction of all roots of algebraic polynomial a family of multi point iterative methods for simultaneous determination of all roots of polynomial equation is obtained this family is corresponding to a family of multi point methods for approximation of only one root of nonlinear equations the convergence analysis and numerical examples are given

improving newton raphson method for nonlinear equations by modified adomian decomposition method in this paper we present some efficient numerical algorithms for solving nonlinear equations based on newton raphson method the modified adomian decomposition method is applied to construct the numerical algorithms some numerical illustrations are given to show the efficiency of algorithms

convergence ball and error analysis of a family of iterative methods with cubic convergence a family of iterative methods with cubic convergence to find approximate solutions of nonlinear equations is proposed the radius of the convergence ball of any iterative method of the family is estimated and quadratic convergence is obtained under the assumption that the first order frechet derivative of the operator involved is lipschitz continuous if the second order frechet derivative of the operator involved is assumed also to be lipschitz continuous cubic convergence of any iterative method of the family is obtained finally some examples are provided to show applications of our theorems

an efficient algorithm for the multivariable adomian polynomials abstract in this article the sum of the series of multivariable adomian polynomials is demonstrated to be identical to a rearrangement of the multivariable taylor expansion of an analytic function of the decomposition series of solutions u 1 u 2 u m about the initial solution components u 1 0 u 2 0 u m 0 of course the multivariable adomian polynomials were developed and are eminently practical for the solution of coupled nonlinear differential equations the index matrices and their simplified forms of the multivariable adomian polynomials are introduced we obtain the recurrence relations for the simplified index matrices which provide a convenient algorithm for rapid generation of the multivariable adomian polynomials another alternative algorithm for term recurrence is established in these algorithms recurrence processes do not require complicated operations such as parametrization expanding and regrouping derivatives etc as practiced in prior art the mathematica program generating the adomian polynomials based on the algorithm in this article is designed

a note on some recent methods for solving nonlinear equations abstract in this note we present some comments on the recent results concerning iterative methods for solving nonlinear equations in the first part we compare a new method n ujevic a method for solving nonlinear equations appl math comput 174 2006 1416 1426 with the newton and ostrowski method including an extensive analysis of numerical results together with the choice of initial approximations and the computational efficiency of the considered methods in the second part we give a list of recently derived root finding methods and we study the question of priority namely we find out that all reviewed methods were already derived at the beginning of the 60s of the last century one of them dates from the 18th century some remarks on the comparison analysis and the application of iteration methods are included

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

one point newton type iterative methods in this paper a unified point of view that includes the most of one point newton type iterative methods for solving nonlinear equations is introduced a simple idea to design iterative methods with quadratic or cubic convergence is also described this idea is extended to construct one point iterative methods of order four in addition several numerical examples are given to illustrate and compare different known methods and some introduced by using this unifying idea

solving nonlinear equations by a new derivative free iterative method we develop a new simple iteration formula which does not require any derivatives of f x for solving a nonlinear equation f x 0 it is proved that the convergence order of the new method is quadratic furthermore the new method can approximate complex roots by several numerical examples we show that the presented method will give desirable approximation to the root without a particularly good initial approximation and be efficient for all cases regardless of the behavior of f x

some multi step iterative methods for solving nonlinear equations in this paper we develop some new iterative methods for solving nonlinear equations by using the techniques introduced in golbabai and javidi 2007 1 and rafiq and rafiullah 2008 20 we establish the convergence analysis of the proposed methods and then demonstrate their efficiency by taking some test problems

approximating the finite hilbert transform via a companion of ostrowski s inequality for function of bounded variation and applications the finite hilbert transform plays an important role in scientific and engineering computing by using a companion of ostrowski s inequality for function of bounded variation we give some new approximations of the finite hilbert transform which may have the better error bounds than the known results obtained via ostrowski type inequality some numerical experiments are also presented

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

experiments in quadratic 0 1 programming we present computational experience with a cutting plane algorithm for 0 1 quadratic programming without constraints our approach is based on a reduction of this problem to a max cut problem in a graph and on a partial linear description of the cut polytope

explicit solutions of nonlinear partial differential equations explicit solutions are calculated by the decomposition method for burger s equation for comparison with other existing procedures such as similarity reduction etc

some nonlinear dynamic integral inequalities on time scales in this paper we study some dynamic integral inequalities with mixed nonlinearities on time scales which provide explicit bounds on unknown functions our results include many existing ones in the literature as special cases and can be used as tools in the qualitative theory of certain classes of dynamic equations with mixed nonlinearities on time scales

numerical method for solving fractional coupled burgers equations in this paper we use the fractional variational iteration method fvim to solve a time and space fractional coupled burgers equations some numerical examples are presented to show the efficiency of considered method a comparison of the proposed method is made with the exact solution adomain decomposition method adm generalized differential transformation method gdtm and homotopy perturbation method hpm

a non iterative method for solving non linear equations abstract in this paper using a hyperbolic tangent function tanh x 0 we develop a non iterative method to estimate a root of an equation f x 0 the problem of finding root is transformed to evaluating an integral and thus we need not take account of choosing initial guess the larger the value of the better the approximation to the root alternatively we employ the signum function sgn x instead of the hyperbolic tangent function which results in an exact formula for the root availability of the present method is shown by some numerical examples for which the traditional newton s method is not appropriate

comparison of the solutions obtained by b spline fem and adm of kdv equation a numerical solution to a generalized korteweg de vries kdv equation is obtained using the galerkin method with quadratic b spline finite element method fem over which the nonlinear term is locally linearized and using the adomian s decomposition method adm test problems concerning the motion and interaction of soliton solutions are used to compare the fem with the adm the present methods extremely well in terms of accuracy efficiency simplicity stability and reliability

on a family of halley like methods to find simple roots of nonlinear equations there are many methods for solving a nonlinear algebraic equation here we introduce a family of halley like methods and show that euler chebyshev and bsc are just members of the family we discuss the conjugacy maps and the effect of the extraneous roots on the basins of attraction

the theoretical foundation of the adomian method abstract in this paper we work out the theoretical basis of the adomian method this powerful method that g adomian has developed in the beginning of the 1980 s supplies analytical approximations to the solution of many kinds of equations thanks to our decomposition theory we justify the practical method and we generalize the convergence results obtained by y cherruault afterward we explain how to solve rigorously equations with linear nonlinear or composed operator and also equations with several terms or with a second member

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

some new volterra fredholm type dynamic integral inequalities on time scales in this paper some new explicit bounds on solutions to a class of new volterra fredholm type dynamic integral inequalities on time scales are established which can be used as effective tools in the study of certain dynamic equations some applications for dynamic equations are also indicated

improvements of the efficiency of some three step iterative like newton methods an improvement of the local order of convergence is presented to increase the efficiency of the iterative method with an appropriate number of evaluations of the function and its derivative the third and fourth order of known two step like newton methods have been improved and the efficiency has also been increased

a new approach to the heat equation an application of the decomposition method abstract the author s decomposition method adomian stochastic systems academic press new york 1983 nonlinear stochastic operator equations academic press new york in press bellman and adomian partial differential equations methods for their treatment and solution reidel dordrecht 1984 adomian j comput appl math 2 1984 225 230 shown elsewhere to provide computable accurate approximate convergent solutions to nonlinear stochastic operator equations is applied to the heat equation

certain improvements of newton s method with fourth order convergence in this paper we present two new schemes one is third order and the other is fourth order these are improvements of second order methods for solving nonlinear equations and are based on the method of undetermined coefficients we show that the fourth order method is more efficient than the fifth order method due to kou et al j kou y li x wang some modifications of newton s method with fifth order covergence j comput appl math 209 2007 146 152 numerical examples are given to support that the methods thus obtained can compete with other iterative methods

finding quasi core with simulated stacked neural networks studying networks is promising for diverse applications we are often interested in exploring significant substructures in different types of real life networks finding cliques which denote a complete subgraph of a graph is one such important problem in network analysis interestingly many real life networks often contain a significant number of almost quasi complete subgraphs which are not entirely complete due to the presence of noise considering these networks as weighted adds further challenges to the problem finding quasi complete subgraphs in weighted graphs has never been formally addressed in this paper we propose a stacked neural network model for finding out the largest quasi complete module core in weighted graphs we show the effectiveness of the proposed approach on dimacs graphs we also highlight its utility in analyzing scientific collaboration networks social networks and biological networks

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

numerical methods for fourth order fractional integro differential equations this paper outlines a reliable strategy for solving linear and nonlinear boundary value problems for fourth order fractional integro differential equations the fractional derivative is considered in the caputo sense the adomian decomposition method is found to be fast and accurate numerical examples are presented to illustrate the efficiency and reliability of the method

adams like techniques for zero finder methods two families of zero finding iterative methods for nonlinear equations are presented we derive them solving an initial value problem using adams like multistep techniques namely adams methods have been used to solve the problem that consists in a differential equation in what appears the inverse function of the one which zero will be computed and the condition given by the value attained by it at the initial approximation performing this procedure several methods of different local orders of convergence have been obtained

a third order newton type method to solve systems of nonlinear equations in this paper we present a third order newton type method to solve systems of nonlinear equations in the first we present theoretical preliminaries of the method secondly we solve some systems of nonlinear equations all test problems show the third order convergence of our method

analytical solution of the bagley torvik equation by adomian decomposition method abstract the fractional derivative has been occurring in many physical problems such as frequency dependent damping behavior of materials motion of a large thin plate in a newtonian fluid creep and relaxation functions for viscoelastic materials the pi d controller for the control of dynamical systems etc phenomena in electromagnetics acoustics viscoelasticity electrochemistry and material science are also described by differential equations of fractional order the solution of the differential equation containing fractional derivative is much involved instead of application of the existing methods an attempt has been made in the present analysis to obtain the solution of bagley torvik equation r l bagley p j torvik on the appearance of the fractional derivative in the behavior of real materials asme j appl mech 51 1984 294 298 i podlubny fractional differential equations academic press san diego ca usa 1999 by the relatively new adomian decomposition method the results obtained by this method are then graphically represented and then compared with those available in the work of podlubny i podlubny fractional differential equations academic press san diego ca usa 1999 a good agreement of the results is observed

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

new iterative methods for nonlinear equations by modified hpm a numerical method based on modified homotopy perturbation method hpm is proposed for solving nonlinear algebric equations it is shown that the proposed method has third order convergence to assess its validity and accuracy the method is applied to solve several test problems

a new approach to nonlinear partial differential equations abstract the author s decomposition method for the solution of operator equations which may be nonlinear and or stochastic is generalized to multidimensional cases

a third order newton type method for nonlinear equations based on modified homotopy perturbation method in this paper we present a new iterative method for solving nonlinear algebric equations by using modified homotopy perturbation method we also discuss the convergence criteria of the present method to assess its validity and accuracy the method is applied to solve several test problems

third order derivative free sph iterative method for solving nonlinear systems the majority of iterative methods to find roots of a function requires the evaluation of derivatives of this function in this paper based on the basic principle of the sph method s kernel approximation a kernel approximation was constructed to compute first and second order derivatives through taylor series expansion derivatives in our proposed method were replaced in a newton like iterative method to obtain a derivative free sph iterative method for solving nonlinear systems to illustrate that the new method has the same order of convergence as the considered iterative method some numerical examples are presented

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

construction of newton like iteration methods for solving nonlinear equations in this paper we present a simple and yet powerful and easily applicable scheme in constructing the newton like iteration formulae for the computation of the solutions of nonlinear equations the new scheme is based on the homotopy analysis method applied to equations in general form equivalent to the nonlinear equations it provides a tool to develop new newton like iteration methods or to improve the existing iteration methods which contains the well known newton iteration formula in logic those all improve the newton method the orders of convergence and corresponding error equations of the obtained iteration formulae are derived analytically or with the help of maple some numerical tests are given to support the theory developed in this paper

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

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

zero finder methods derived using runge kutta techniques abstract in this paper some families of zero finding iterative methods for nonlinear equations are presented the key idea to derive them is to solve an initial value problem applying runge kutta techniques more explicitly these methods are used to solve the problem that consists in a differential equation in what appears the inverse function of the one which zero will be computed and the condition given by the value attained by it at the initial approximation carrying out this procedure several families of different orders of local convergence are obtained furthermore the efficiency of these families are computed and two new families using like newton s methods that improve the most efficient one are also given

newton like iterative methods for solving system of non linear equations abstract homotopy perturbation method hpm is applied to construct a new family of newton like iterative methods for solving system of non linear equations comparison of the result obtained by the present method with newton raphson method reveals that the accuracy and fast convergence of the new method

the decomposition method for ordinary differential equations with discontinuities in this paper the decomposition method is applied to the initial value problem ivp for ordinary differential equations with discontinuities for both linear and nonlinear cases

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 family of methods for solving nonlinear equations we present a family of methods for solving nonlinear equations some well known classical methods and their modifications belong to our family for example newton potra ptak chebyshev halley and ostrowski s methods convergence analysis shows that our family contains methods of convergence order from 2 to 4 all our fourth order methods are optimal in terms of the kung and traub conjecture several examples are presented and compared

comparison of the solutions obtained by adomian decomposition and wavelet galerkin methods of boundary value problems abstract in this paper we will compare the performance of adomian decomposition method and the wavelet galerkin method applied to the solution of boundary value problems involving non homogeneous heat and wave equations it is shown that the adomian decomposition method in many instances gives better results in the wavelet galerkin solutions daubechies six wavelets are used because they give better results than those of lower degree wavelets the results are then compared with those obtained using the adomian decomposition method although the adomian decomposition solution required slightly more computational effort than the wavelet galerkin solution it resulted in more accurate results than the wavelet galerkin method

a new family of iterative methods for solving system of nonlinear algebric equations abstract homotopy perturbation method hpm is applied to construct a new iterative method for solving system of nonlinear algebric equations comparison of the result obtained by the present method with that obtained by revised adomian decomposition method hossein jafari varsha daftardar gejji appl math comput 175 2006 1 7 reveals that the accuracy and fast convergence of the new method

solving a multi order fractional differential equation using adomian decomposition abstract an algorithm has been developed to convert the multi order fractional differential equation d y t f t y t d 1 y t d n y t y k 0 c k k 0 m where m d denotes caputo fractional derivative of order into a system of fractional differential equations further adomian decomposition method has been employed to solve the system of fractional differential equations some illustrative examples are presented

an analysis of the properties of the variants of newton s method with third order convergence for the last five years the variants of the newton s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non linear equations these methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives in this paper we investigate about the relationship between these methods which are in fact based on the approximation of the second order derivative present in the third order limited taylor expansion we also prove that they are different forms of the halley method and are all contractive iterative methods in a common neighbourhood we extend some of these variants to multivariate cases and prove their respective local cubic convergence from their corresponding linear models

geometric constructions of iterative functions to solve nonlinear equations in this paper we present the geometrical interpretation of several iterative methods to solve a nonlinear scalar equation in addition we also review the extension to general banach spaces and some computational aspects of these methods

two point iterative methods for solving nonlinear equations in this study a new root finding technique for solving nonlinear equations is proposed then two new more algorithms are derived from this new technique by employing the adomian decomposition method adm these three algorithms require two starting values that do not necessarily bracketing the root of a given nonlinear equation however when the starting values are closed enough or bracketed the root then the proposed methods converge to the root faster than the secant method another advantage over all iterative methods is that the proposed methods usually converge to two distinct roots when the handled nonlinear equation has more than one root that is the odd iterations of the new techniques converge to a root and the even iterations converge to another root some numerical examples including a sine polynomial equation are solved by using the proposed methods and compared with the secant method perfect agreements were found

numerical study of modified adomian s method applied to burgers equation the application of adomian s decomposition method to partial differential equations when the exact solution is not reached demands the use of truncated series but the solution s series may have small convergence radius and the truncated series may be inaccurate in many regions in order to enlarge the convergence domain of the truncated series pade approximants pas to the adomian s series solution have been tested and applied to partial and ordinary differential equations with good results in this paper pas both in x and t directions applied to the truncated series solution given by adomian s decomposition technique for burgers equation are tested numerical and graphical illustrations show that this technique can improve the accuracy and enlarge the domain of convergence of the solution it is also shown in this paper that the application of adomian s method to the ordinary differential equations set arising from the discretization of the spatial derivatives by finite differences the so called method of lines may reduce the convergence domain of the solution s series

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

a simple simulated annealing algorithm for the maximum clique problem abstract simulated annealing technique has mostly been used to solve various optimization and learning problems and it is well known that the maximum clique problem is one of the most studied np hard optimization problems owing to its numerous applications in this note a simple simulated annealing algorithm for the maximum clique problem is proposed and tested on all 80 dimacs maximum clique instances although it is simple the proposed simulated annealing algorithm is efficient on most of the dimacs maximum clique instances the simulation results show that the proposed simulated annealing algorithm outperforms a recent efficient simulated annealing algorithm proposed by xu and ma and the solutions obtained by the proposed simulated annealing algorithm have the equal quality with those obtained by a recent trust region heuristic algorithm of stanislav busygin

an algorithm for adomian decomposition method in this paper a reliable technique for calculating adomian polynomials for nonlinear operators is developed the algorithm is fulfilled with symbolic computation so that the adomian decomposition methods for solving differential equations can be mechanized in maple ten examples are presented to illustrate the implementation of the program

some delay integral inequalities on time scales in this paper using gronwall s inequality we investigate some delay integral inequalities on time scales which provide explicit bounds on unknown functions our results unify and extend some delay integral inequalities and their corresponding discrete analogues the inequalities given here can be used as tools in the qualitative theory of certain classes of delay dynamic equations on time scales

new iterative methods abstract in this paper we present a new three step predictor corrector type iterative method for finding simple and real roots of a non linear equation in one variable i e f x 0 experiments show that our new method is more efficient than the other known methods a comparison of the proposed method with other methods reveals that the new method performs better as shown in table 2

adomian decomposition method for solution of nonlinear differential algebraic equations in m m hosseini adomian decomposition method with chebyshev polynomials appl math comput in press an efficient modification of the adomian decomposition method was presented by using chebyshev polynomials also in m m hosseini adomian decomposition method for solution of differential algebraic equations j comput appl math in press solution of linear differential algebraic equations was considered by adomian decomposition method in this paper standard and modified adomian decomposition methods are applied to non linear differential algebraic equations the schemes are tested for some examples and the results demonstrate reliability and efficiency of the proposed methods

some modification of newton s method by the method of undetermined coefficients in this paper we construct some modifications of newton s method for solving nonlinear equations which is based on the method of undetermined coefficients it is shown by way of illustration that the method of undetermined coefficients is a promising tool for developing new methods and reveals its wide applicability by obtaining some existing methods as special cases two new sixth order methods are developed numerical examples are given to support that the methods thus obtained can compete with other iterative methods

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 ostrowski gruss type inequality on time scales we derive a new inequality of ostrowski gruss type on time scales by using the gruss inequality on time scales and thus unify corresponding continuous and discrete versions we also apply our result to the quantum calculus case

a parallel improvement algorithm for the bipartite subgraph problem the authors propose the first parallel improvement algorithm using the maximum neural network model for the bipartite subgraph problem the goal of this np complete problem is to remove the minimum number of edges in a given graph such that the remaining graph is a bipartite graph a large number of instances have been simulated to verify the proposed algorithm with the simulation result showing that the algorithm finds a solution within 200 iteration steps and the solution quality is superior to that of the best existing algorithm the algorithm is extended for the k partite subgraph problem where no algorithm has been proposed

diamond α weighted ostrowski type and gruss type inequalities on time scales in this paper we obtain some weighted ostrowski type and gruss type inequalities on time scales by using the recent theory of combined dynamic derivatives on time scales these results extend some known results in the literature and give some other interesting inequalities as special cases

notes on the diamond α dynamic derivative on time scales abstract various dynamic derivative formulae have been proposed in the development of a time scales calculus with the goal of unifying continuous and discrete analysis recent discussions of combined dynamic derivatives in particular the derivative defined as a linear combination of the and the derivatives have promised improved approximation formulae for computational applications this paper presents an equivalent definition of the functions without reference to the existing and derivatives examines the status of the as a dynamic derivative and its properties relative to the and derivatives and compares data obtained using the various dynamic derivatives as approximation formulae in computational experiments a integral case is investigated

iterative methods for solving nonlinear equations with finitely many roots in an interval in this paper we consider a nonlinear equation f x 0 having finitely many roots in a bounded interval based on the so called numerical integration method b i yun a non iterative method for solving non linear equations appl math comput 198 2008 691 699 without any initial guess we propose iterative methods to obtain all the roots of the nonlinear equation in the result an algorithm to find all of the simple roots and multiple ones as well as the extrema of f x is developed moreover criteria for distinguishing zeros and extrema are included in the algorithm availability of the proposed method is demonstrated by some numerical examples

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

numerical study of lorenz s equation by the adomian method abstract in this paper we use the decomposition method of adomian for solving differential systems coming from physics meteorology we also give a comparison between the runge kutta method and the decomposition technique furthermore we reconfirm the famous butterfly effect

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

modified homotopy perturbation method for nonlinear equations and comparison with adomian decomposition method abstract in this paper we present some efficient numerical algorithms for solving nonlinear equations based on newton raphson method by using modified homotopy perturbation method the modified adomian decomposition method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method appl math comput 145 2003 887 893 is compared with new algorithms some numerical illustrations are given to show the efficiency of algorithms

a fourth order derivative free algorithm for nonlinear equations a two step derivative free iterative algorithm is presented for solving nonlinear equations error analysis shows that the algorithm is fourth order with efficiency index equal to 1 5874 a lot of numerical results show that the algorithm is effective and is preferable to some existing derivative free methods in terms of computation cost

solving a system of nonlinear fractional differential equations using adomian decomposition adomian decomposition method has been employed to obtain solutions of a system of nonlinear fractional differential equations dxiyi x ni x y1 yn yi k 0 cki 0 k i 1 i n and dxi denotes caputo fractional derivative some examples are solved as illustrations using symbolic computation

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

iterative methods to nonlinear equations homotopy perturbation method is applied to construct a new iterative method for solving nonlinear algebraic equations the convergence of the new scheme is proposed an 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 the new method

the decomposition method for stiff systems of ordinary differential equations in this paper the decomposition method is applied to initial value problems for systems of ordinary differential equations in both linear and nonlinear cases focusing our interest in stiff problems