solution of a system of nonlinear equations by adomian decomposition method in this paper the adomian decomposition method is applied to solve a system of nonlinear equations convergence of the method is proved and some examples are presented to illustrate the method

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

avoiding the computation of the second fre chet derivative in the convex acceleration of newton s method we introduce a new two step method to approximate a solution of a nonlinear operator equation in a banach space an existence uniqueness theorem and error estimates are provided for this iteration using newton kantorovich type assumptions and a technique based on a new system of recurrence relations for a special choice of the parameter involved we use our method is of fourth order

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

revised adomian decomposition method for solving a system of nonlinear equations a modification of adomian decomposition method is suggested and used for solving a system of nonlinear equations which yields a series solution with accelerated convergence illustrative examples have been presented to demonstrate the method and the results obtained are compared with those derived from the standard adomian decomposition method

variants of newton s method using fifth order quadrature formulas abstract some variants of newton s method are developed in this work in order to solve nonlinear equations depending on one or several variables based in rules of quadrature of fifth order we prove the third or fifth order of convergence of these methods for dimension one and the second or third order in several variables depending on the behaviour of the second derivative moreover different numeric tests confirm or improve theoretic results and allow us to compare these variants with newton s classical method

a note on the local convergence of iterative methods based on adomian decomposition method and 3 node quadrature rule abstract darvishi and barati m t darvishi a barati super cubic iterative methods to solve systems of nonlinear equations appl math comput 2006 10 1016 j amc 2006 11 022 derived a super cubic method from the adomian decomposition method to solve systems of nonlinear equations the authors showed that the method is third order convergent using classical taylor expansion but the numerical experiments conducted by them showed that the method exhibits super cubic convergence in the present work using ostrowski s technique based on point of attraction we show that their method is in fact fourth order convergent we also prove the local convergence of another fourth order method from 3 node quadrature rule using point of attraction

variants of newton s method for functions of several variables some variants of newton s method are developed in this work in order to solve systems of nonlinear equations based in trapezoidal and midpoint rules of quadrature we prove the quadratic convergence of one of these methods moreover different numeric tests confirm theoretic results and allow us to compare these variants with newton s classical method

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

single step formulas and multi step formulas of the integration method for solving the initial value problem of ordinary differential equation abstract adam bashforth method and adam moulton method are two known multi step methods for finding the numerical solution of the initial value problem of ordinary differential equation these two methods used the newton backward difference method to approximate the value of f x y in the integral equation which is equivalent to the given differential equation

extended newton s method for a system of nonlinear equations by modified adomian decomposition method abstract in this paper we present some efficient numerical algorithms for solving a system of two nonlinear equations with two variables based on newton s method the modified adomian decomposition method is applied to construct the numerical algorithms some numerical illustrations are given to show the efficiency of algorithms

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

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

third order methods from quadrature formulae for solving systems of nonlinear equations we extend to p dimensional problems a modification of the newton method based on quadrature formulas of order at least one which produces iterative methods with order of convergence three a general error analysis providing the higher order of convergence is given these new methods may be more efficient then other third order methods as they do not require the use of the second order frechet derivative

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

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

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

third order iterative methods free from second derivative for nonlinear systems in this work we present a family of predictor corrector methods free from second derivative for solving nonlinear systems we prove that the methods of this family are of third order convergence we also perform numerical tests that allow us to compare these methods with newton s method in addition the numerical examples improve theoretical results showing super cubic convergence for some methods of this family

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 iterative method with cubic convergence 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 this new method new method can be viewed as an improvement of the previously known iterative methods

adomian s decomposition method applied to systems of nonlinear algebraic equations in this paper an algorithm based on adomian s decomposition method is developed to approximate the solution of systems of nonlinear algebraic equations f x 0 special cases of the system of nonlinear equations are solved using the algorithm of the decomposition method it turns out that the convergence of this algorithm is rapid the decomposition method has the advantage of being more concise for numerical purposes

an iterative method for solving nonlinear functional equations an iterative method for solving nonlinear functional equations viz nonlinear volterra integral equations algebraic equations and systems of ordinary differential equation nonlinear algebraic equations and fractional differential equations has been discussed

fast reliable simulations of secondary settling tanks in wastewater treatment with semi implicit time discretization the bio kinetic and sedimentation processes of wastewater treatment plants can be modelled by a large system of coupled nonlinear ordinary and partial differential equations odes and pdes the subprocess of continuous sedimentation which contains concentration discontinuities is modelled by a degenerate parabolic conservation pde with spatially discontinuous coefficients a spatial discretization of this pde described in brger etal 2013 results in a large system of method of lines odes for the entire plant and simulation can be performed by integration in time in practice standard time integration methods available in commercial simulators are often used shortages of such methods are here shown such as the smearing of shock waves by rungekutta methods and long execution times a semi implicit time discretization which is described in detail provides substantially shorter computational times and is more efficient than standard methods

new nonlinear coherent states based on hypergeometric type operators the main goal of this paper is to present an alternative method to construct new kinds of nonlinear coherent states to do this we first establish a class of hypergeometric type of generalized displacement operators 1fr 0 0 1 r 1 za act on the vacuum state of the harmonic oscillator and generate normalized quantum states of the fock space which admit a resolution of the identity through a positive definite measure on the complex plane furthermore realization of the compact form of these states as functions of the position coordinate x for r 2 leads to a generating function of the hermite polynomials in terms of the modified bessel function finally studying some statistical characters reveals that they have indeed non classical features such as squeezing an anti bunching effect and sub poissonian statistics too

on iterative methods for nonlinear equations several iterative methods have been suggested and analyzed for solving nonlinear equation f x 0 all these methods can be classified as one step and two step methods in this paper we have suggested and analyzed several two step methods for solving nonlinear equations we have also shown that these two step methods are quadratically convergent several numerical examples are given to illustrate this comparison our results can be viewed as important refinement and improvement of the previously known results

convergence analysis of a variant of the newton method for solving nonlinear equations the paper presents a convergence analysis of a modified newton method for solving nonlinear systems of equations the convergence results show that this method converges cubically in the nonsingular case and linearly with the rate 3 8 under some sufficient conditions when the jacobian is singular at the root the convergence theory is used to analyze the convergence behavior when the modified newton method is applied to a nonsymmetric algebraic riccati equation arising in transport theory numerical experiment confirms the theoretical results

some iterative methods for solving a system of nonlinear equations in this paper we suggest and analyze two new two step iterative methods for solving the system of nonlinear equations using quadrature formulas we prove that these new methods have cubic convergence several numerical examples are given to illustrate the efficiency and the performance of the new iterative methods these new iterative methods may be viewed as an extension and generalizations of the existing methods for solving the system of nonlinear equations