a study of convergence on the newton homotopy continuation method the traditional newton method is a well known and popular method for solving non linear equation it has high efficient in the convergence speed however we always need to guess the initial value in the iteration process good initial guess value can solve the equation quickly bad initial guess value usually will yield divergence homotopy continuation method is a kind of perturbation method it can guarantee the answer by a certain path if we choose the auxiliary homotopy function or call start system well this paper presents some useful rules for the choice of the auxiliary homotopy function to avoid the problem of divergence of traditional newton method

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

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

new iterative technique for solving nonlinear equations various problems of pure and applied sciences can be studied in the unified frame work of the nonlinear equations in this paper a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique the convergence of the proposed methods is proved it is shown that the new family contains several well known iterative methods as special case for the implementation and performance of the new methods a nonlinear equation arising in the population model and another one arising in the motion of a particle on inclined plane is solved

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

homotopy perturbation method for a type of nonlinear coupled equations with parameters derivative abstract in this paper homotopy perturbation method is directly extended to investigate nonlinear coupled equations with parameters derivative and to derive their numerical solutions these nonlinear coupled equations with parameters derivative contain many important mathematical physics equations and reaction diffusion equations by choosing different values of the parameters in general formal numerical solutions as a result a very rapidly convergent series solution is obtained the efficiency and accuracy of the method are verified by using two famous examples coupled burgers and mkdv equations numerical solutions show that good results have been achieved

a new hybrid iteration method for solving algebraic equations abstract a new hybrid iteration method the hybrid s name was used by luo xing guo luo applied mathematics and computation 171 2 2005 1171 1183 has been proposed for solving a non linear algebraic equation f x 0 by using taylor s theorem in this paper we proposed a new hybrid iteration method and we show by one equation that this new hybrid iteration method is more quickly convergent than newton s method and hence than hybrid iteration method

modified iterative methods with cubic convergence for solving nonlinear equations abstract in this paper we suggest and analyze two new predictor corrector methods for solving nonlinear equations f x 0 these methods can be considered as two step methods we show that these methods have cubic convergence using this one of the new methods real or complex roots for certain nonlinear equations can be obtained several numerical examples are given to illustrate the efficiency and performance of the new methods our method can be considered as an improvement of the existing methods and can be viewed as an alternative to the existing methods

the solution of multipoint boundary value problems by the optimal homotopy asymptotic method in this work we solve multipoint boundary value problems using the optimal homotopy asymptotic method oham the proposed method is tested upon several problems from the literature and the results are compared with the available exact solution this method provides easy tools to control the convergence region of approximating solution series where ever necessary

left symmetric algebras from linear functions abstract in this paper some left symmetric algebras are constructed from linear functions they include a kind of simple left symmetric algebras and some examples appearing in mathematical physics their complete classification is also given which shows that they can be regarded as generalization of certain two dimensional left symmetric algebras

a new iteration method for solving algebraic equations in this paper a nonlinear algebraic equation f x 0 by applying taylor s theorem is converted into a coupled iteration systeml x n 1 g x n 0andg x n f x n l x n wherel x ax 2 bx c the formula is of high convergence some examples are given

a new iteration method with cubic convergence to solve nonlinear algebraic equations abstract in this paper a new iteration scheme is proposed to solve the roots of an algebraic equation f x 0 given an initial guess x0 the roots of the equation can be obtained using the following iteration scheme x n 1 x n f x n f 2 x n 2 f x n f x n f x n this iteration scheme has unique convergence characteristics different from the well known newton s method it is shown that this iteration method has cubic local convergence in the neighborhood of the root using this scheme real or complex roots for specific algebraic equations can be found because there are two iteration directions for a given initial guess two solutions can be found for certain algebraic equations with multiple roots examples are presented and compared with other methods

evaluation of the distribution function of the limited information maximum likelihood estimator the distributions of the limited information maximum likelihood estimator for the coefficient of one endogenous variable are evaluated numerically tables are given for enough values of the parameters to cover all cases of interests comparisons are made with the two stage least squares estimator

dynamics of a family of third order iterative methods that do not require using second derivatives the purpose of this article is to present results that amount to a description of the conjugacy classes of three third order root finding iterative methods that do not require the use of second derivatives for their formulation for complex polynomials of degrees two three and four for degrees two and three a full description of the conjugacy classes is accomplished in each case by a one parameter family of polynomials this is done in such a way that when one applies one of these three root finding iterative methods to the elements of these parametrized families a family of iterative methods is obtained in such a way that its dynamics represents up to conjugacy the dynamics of the corresponding iterative root finding method applied to any complex polynomial having the same degree for degree four analogous partial results are obtained

application of the optimal homotopy asymptotic method to squeezing flow in this paper axisymmetric flow of two dimensional incompressible fluids is studied the optimal homotopy asymptotic method oham is applied to derive a solution of the reduced fourth order nonlinear boundary value problem for comparison the same problem is also solved by the perturbation method pm the homotopy perturbation method hpm 3 and the homotopy analysis method ham 4 oham is parameter free and provides better accuracy at lower order of approximation moreover we can easily adjust and control the convergence region as a result it is concluded that the new technique oham shows fast convergence simplicity of application and efficiency

new family of iterative methods for nonlinear equations in this paper we suggest and analyze a new family of iterative methods for solving nonlinear equations using the system of coupled equations coupled with decomposition technique several numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

new iterative schemes for nonlinear equations in this paper we suggest and analyze a new iterative method for solving nonlinear equations by using a new decomposition method we also discuss the convergence criteria of these iterative methods several numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

some numerical methods for solving nonlinear equations by using decomposition technique in this paper we use the system of coupled equations involving an auxiliary function together with decomposition technique to suggest and analyze some new classes of iterative methods for solving nonlinear equations these new methods include the halley method and its variant forms as special cases various numerical examples are given to illustrate the efficiency and performance of the new methods these new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations

new iterative methods for solving nonlinear equation by using homotopy perturbation method in this paper we suggest and analyze a new class of iterative methods for solving nonlinear equations by using the homotopy perturbation method convergence of their method is also considered here we also discuss the efficiency index and computational order of convergence of new methods several numerical examples are given to illustrate the efficiency and performance of these new methods these new iterative methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations

a fourth order iterative method for solving nonlinear equations the present paper illustrates an iterative numerical method to solve nonlinear equations of the form f x 0 especially those containing the partial and non partial involvement of transcendental terms comparative analysis shows that the present method is faster than newton raphson method hybrid iteration method new hybrid iteration method and others cost is also found to be minimum than these methods the beauty in our method can be seen because of the optimization in important effecting factors i e lesser number of iteration steps lesser number of functional evaluations and lesser value of absolute error in final as well as in individual step as compared to the other methods this work also demonstrates the higher order convergence of the present method as compared to others without going to the computation of second derivative

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 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

a unified algebraic approach to the classical yang baxter equation in this paper the different operator forms of the classical yang baxter equation are given in the tensor expression through a unified algebraic method it is closely related to left symmetric algebras which play an important role in many fields in mathematics and mathematical physics by studying the relations between left symmetric algebras and the classical yang baxter equation we can construct left symmetric algebras from certain classical r matrices and conversely there is a natural classical r matrix constructed from a left symmetric algebra which corresponds to a parakahler structure in geometry moreover the former in a special case gives an algebraic interpretation of the left symmetry as a lie bracket left twisted by a classical r matrix

three step iterative methods for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations we show that this new iterative method has third order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

some variant of newton s method with third order convergence we present a new modification of the newton s method which produces iterative methods with order of convergence three a general error analysis providing the higher order of convergence is given and the best efficiency in term of function evaluations of two of this new methods is provided

efficient method for solving a system of nonlinear equations various problems of pure and applied sciences can be studied in the unified frame work of the system of nonlinear equations by using decomposition technique in conjunction with the coupled system of equations we develop new iterative method for solving a system of nonlinear equations which has better efficiency index we prove the fifth order convergence of the proposed method we provide the comparison of efficiency index with some other well known methods for the implementation and performance of the new method we solve the kinematic synthesis problem for steering chandrasekhar integral equation and combustion problem for a temperature of 3000 c and compare the results with some existing methods

non abelian phase spaces for a vector space v its phase space t v is the vector space v v together with the canonical symplectic form on it since the vector space is the same as an abelian lie algebra the natural question is given a lie algebra g does there exist a phase space t g in general the answer is negative below for a large class of lie algebras g the phase space t g is constructed three examples are treated in detail g gl v g d rn the lie algebra of vector fields on rn and current algebras

on the dynamics of the euler iterative function abstract the dynamics of euler s third order iterative method which is used to find roots of non linear equations applied to complex polynomials of degrees three and four is studied the conjugacy classes of this method are found explicitly

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

iterative methods with fourth order convergence for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations involving only first derive of the function using a new decomposition technique which is due to noor m aslam noor numerical analysis and optimization lecture notes comsats institute of information technology islamabad pakistan 2006 m aslam noor new iterative schemes for nonlinear equations appl math comput in press and noor and noor m aslam noor k inayat noor some iterative schemes for nonlinear equations appl math comput in press we show that this new iterative method has fourth order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

on modified newton methods for solving a non linear algebraic equations abstract in this paper we present a new modified newton method for solving a non linear algebraic equation by using the well known nedzhibov s method d k r babajee m z dauhoo an analysis of the properties of the variants of newton s method with third order convergence applied mathematics and computation 183 1 2006 659 684 we proposed a new iteration method and we show by one equation that this new iteration method is more quickly convergence than newton s 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

fifth order iterative methods for solving nonlinear equations abstract in this paper we suggest and analyze a new two step iterative method for solving nonlinear equation f x 0 by rewriting the given nonlinear equation as a coupled system of equations and using the taylor series it is shown that this new iterative method is of fifth order several examples are given to illustrate its performance and efficiency comparison with other methods is also given this method can be viewed as an improvement of the halley s method

higher order iterative schemes for nonlinear equations using decomposition technique in this paper we suggest and analyze some unique recurrence relations which can generate different classes of iterative methods for solving nonlinear equations using the system of coupled equations together with decomposition technique by using an auxiliary function various numerical examples are given to illustrate the efficiency and performance of the newly suggested methods these new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations

new iterative technique for solving a system of nonlinear equations various problems of pure and applied sciences can be studied in the unified frame work of the system of nonlinear equations in this paper a new family of iterative methods for solving a system of nonlinear equations is developed by using a new decomposition technique the convergence of the new methods is proved efficiency index of the proposed methods is discussed and compared with some other well known methods the upper bounds of the error and the radius of convergence of the methods are also found for the implementation and performance of the new methods the combustion problem streering problem and van der pol equation are solved and the results are compared with some existing methods several new iterative methods are derived from the general iterative scheme using the ideas and techniques of this paper one may be able to suggest and investigate a wide class of iterative methods for solving the system of nonlinear equations this is another direction of future research

an efficient fifth order method for solving systems of nonlinear equations in this paper we present a three step iterative method of convergence order five for solving systems of nonlinear equations the methodology is based on the two step homeier s method with cubic convergence homeier 2004 computational efficiency in its general form is discussed and a comparison between the efficiency of proposed technique and existing ones is made the performance is tested through numerical examples moreover theoretical results concerning order of convergence and computational efficiency are verified in the examples it is shown that the present method has an edge over existing methods particularly when applied to large systems of equations

from rota baxter algebras to pre lie algebras rota baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics rota baxter algebras provide a construction of pre lie algebras from associative algebras in this paper we give all rota baxter operators of weight 1 on complex associative algebras in dimension 3 and their corresponding pre lie algebras

asymptotic probability concentrations and finite sample properties of modified liml estimators for equations with more than two endogenous variables this paper investigates the distributional properties of a class of modified limited information maximum likelihood liml estimators it is shown that the asymptotic distributions of these estimators are more concentrated than those of the modified liml estimators suggested by fuller additionally the results of an extensive monte carlo investigation of the finite sample properties of the proposed estimators show that when the equation of interest has more than two endogenous variables the liml estimator is often highly inefficient so that substantial gains in precision are realized by using the modified estimators in place of the liml estimator

modules and morita theorem for operads associative rings a b are called morita equivalent when the categories of left modules over them are equivalent we call two classical linear operads p q morita equivalent if the categories of algebras over them are equivalent we transport a part of morita theory to the operadic context by studying modules over operads as an application of this philosophy we consider an operadic version of the sheaf of linear differential operators on a super manifold m and give a comparison theorem between algebras over this sheaf on m and m red

on a class of quadratically convergent iteration formulae in this paper a new class of iterative formulae having quadratic convergence is presented furthermore these algorithms are comparable to the well known method of newton and the computed results support this theory

the automorphisms of novikov algebras in low dimensions novikov algebras were introduced in connection with poisson brackets of hydrodynamic type and hamiltonian operators in the formal variational calculus they also correspond to a class of vertex algebras an automorphism of a novikov algebra is a linear isomorphism satisfying xy x y which keeps the algebraic structure the set of automorphisms of a novikov algebra is a lie group whose lie algebra is just the novikov algebra s derivation algebra the theory of automorphisms plays an important role in the study of novikov algebras in this paper we study the automorphisms of novikov algebras we get some results on their properties and classification in low dimensions these results are fundamental in a certain sense and they will serve as a guide for further development moreover we apply these results to classify gel fand dorfman bialgebras and novikov poisson algebras these results also can be used to study certain phase spaces and geometric classical r matrices

the numerical values of some key parameters in econometric models abstract in the case of two endogenous variables exogenous predetermined variables and normally distributed disturbances the distributions of the two stage least squares tsls and limited information maximum likelihood liml estimators can be compared on the basis of three key parameters the non centrality parameter a standardization of the structural coefficient and the number of excluded exogenous variables in this paper the values of these parameters are estimated in eleven structural equations from various actual econometric models the distribution functions of the normalized tsls and liml estimators are given for the first two key parameters set at approximately their trimmed means and the third at its median

he s parameter expanding methods for strongly nonlinear oscillators ji huan he s work on asymptotic techniques is briefly reviewed and his parameter expanding methods including modified lindstedt poincare method and bookkeeping parameter method are discussed in detail some remarkable virtues of the methods are exploited and their applications are illustrated

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

a note on the new iteration method for solving algebraic equations in ji huan he a new iteration method for solving algebraic equations appl math comput 135 2003 81 84 a new iteration method for solving algebraic equations has been proposed in this paper we show for one equation which given by the author and some other equations that the new iteration method fails to obtain expected results hence in contrast to previous claims it is no more quickly convergent than newton s method and may in fact be failed

a sixth order method for nonlinear equations abstract in this paper a sixth order method is developed by extending a third order method of weerakoon and fernando s weerakoon t g i fernando a variant of newton s method with accelerated third order convergence appl math lett 13 2000 87 93 for finding the real roots of nonlinear equations in r starting with a suitably chosen x 0 the method generates a sequence of iterates converging to the root the convergence analysis is provided to establish its sixth order of convergence in terms of computational cost it requires evaluations of only two functions and two first derivatives per iteration this implies that efficiency index of our method is 1 565 our method is comparable with the methods of neta b neta a sixth order family of methods for nonlinear equations intern j computer math 7 1979 157 161 and that of kou and li jisheng kou yitian li an improvement of jarratt method appl math comput 189 2007 1816 1821 it does not require the evaluation of the second order derivative of the given function as required in the family of chebyshev halley type methods jisheng kou xiuhua wang sixth order variants of chebyshev halley methods for solving non linear equations appl math comput 190 2007 1839 1843 jisheng kou on chebyshev halley methods with sixth order convergence for solving non linear equations appl math comput 190 2007 126 131 the efficacy of the method is tested on a number of numerical examples it is observed that our method takes less number of iterations than newton s method and the method of weerakoon and fernando on comparison with the other sixth order methods it behaves either similarly or better for the examples considered