shock peakon and shock compacton solutions for k p q equation by variational iteration method by variational iteration method we obtain new solitary solutions for non linear dispersive equations particularly shock peakon solutions in k 2 2 equation and shock compacton solutions in k 3 3 equation are found by this simple method these two types of solutions are new solitary wave solutions which have the shapes of shock solutions and compacton solutions or peakon solutions

he s variational iteration method for treating nonlinear singular boundary value problems this paper applies he s variational iteration method for solving nonlinear singular boundary value problems the solution process is illustrated and various physically relevant results are obtained comparison of the obtained results with exact solutions shows that the method used is an effective and highly promising method for treating various classes of both linear and nonlinear singular boundary value problems

numerical method for non linear wave and diffusion equations by the variational iteration method this paper applies he s variational iteration to the wave equations in an infinite one dimensional medium and some non linear diffusion equations a suitable choice of an initial solution can lead to the needed exact solution by a few iterations copyright 2007 john wiley sons ltd

a note on optimal homotopy asymptotic method for the solutions of fractional order heat and wave like partial differential equations optimal homotopy asymptotic method oham is prolifically implemented to find the optimal solutions of fractional order heat and wave like equations we inspect the competence of the method by examining fractional order time dependent partial differential equations it is observed that oham is a prevailing and convergent method for the solutions of linear and nonlinear fractional order time dependent partial differential problems the numerical results rendering that the applied method is explicit effective and easy to use for handling more general fractional order heat and wave like models

variational iteration method and homotopy perturbation method for nonlinear evolution equations he s variational iteration and homotopy perturbation methods are applied to various evolution equations to assess the accuracy of the solutions we compare the results with the exact solutions revealing that both methods are capable of solving effectively a large number of nonlinear differential equations with high accuracy

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

numerical simulation of equal width wave equation by means of the variational iteration method the solution of the equal width wave equation is numerically obtained and compared with that obtained by the adomian decomposition method numerical results show that the variational iteration method can readily be implemented with excellent accuracy to nonlinear equations

improvement of he s variational iteration method for solving systems of differential equations in recent years a lot of attention from researchers has been attracted to the various aspects of the well known he s variational iteration method this method is a very powerful method for solving a large amount of problems it provides a sequence which converges to the solution of the problem without discretization of the variables in this work an idea is proposed that accelerates the convergence of the sequences which result from the variational iteration method for solving systems of differential equations illustrative examples are presented to show the validity of the new method

computing eigenelements of boundary value problems with fractional derivatives variational iteration method has been successfully implemented to handle linear and nonlinear differential equations the main property of the method is its flexibility and ability to solve nonlinear equations accurately and conveniently in this paper first a general framework of the variational iteration method is presented for analytic treatment of differential equations of fractional order where the fractional derivatives are described in caputo sense second the new framework is used to compute approximate eigenvalues and the corresponding eigenfunctions for boundary value problems with fractional derivatives numerical examples are tested to show the pertinent features of this method this approach provides a new way to investigate eigenvalue problems with fractional order derivatives

random initial imperfections of structures abstract this paper is a theoretical study on random initial imperfections of structures the explicit form of probability density function of the load bearing capacity critical load of structures is derived for random initial imperfections based on a decomposition of the space of imperfection vectors into two orthogonal subspaces the subspace that asymptotically affects the load bearing capacity and the other that does not tight bounds on the range of load bearing capacity are presented for various types of simple critical points by means of the asymptotic theory of statistics we show the inefficiency of a conventional random method that approximates the minimum loadhearing capacity by the minimum load for a number of random initial imperfections the theoretical and empirical probability distribution functions for simple truss structures are compared to show the validity and effectiveness of the present method

on random imperfections for structures of regular polygonal symmetry a theoretical study is made on the effect of random initial imperfections on the load bearing capacities of structures of regular polygonal symmetry the group theoretic method is employed to implement the symmetry in the formulation in view of the concept of critical initial imperfection the explicit form of probability density function of the load bearing capacity of structures is derived for random initial imperfections in particular tight bounds on the range of load bearing capacity are presented for various types of simple and double critical points the theoretical and empirical probability distribution functions are compared for simple truss structures to show the validity and effectiveness of the present method

application of the variational iteration method to the whitham broer kaup equations explicit traveling wave solutions including blow up and periodic solutions of the whitham broer kaup equations are obtained by the variational iteration method moreover the results are compared with those obtained by the adomian decomposition method revealing that the variational iteration method is superior to the adomian decomposition method

modified variational iteration method nonlinear homogeneous initial value problem the modified variational iteration method is applied for analytical treatment of nonlinear homogeneous initial value problem the modified variational iteration method accelerates the convergence of the power series solution and reduces the size of work a comparison between modified variational iteration method mvim and variational iteration method vim was made the comparison enhances the use of the modified variational iteration method if we wish to obtain an approximate power series solution that converges faster to the closed form solution the method is very simple and easy

the variational iteration method an efficient scheme for handling fractional partial differential equations in fluid mechanics variational iteration method has been used to handle linear and nonlinear differential equations the main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently in this work a general framework of the variational iteration method is presented for analytical treatment of fractional partial differential equations in fluid mechanics the fractional derivatives are described in the caputo sense numerical illustrations that include the fractional wave equation fractional burgers equation fractional kdv equation fractional klein gordon equation and fractional boussinesq like equation are investigated to show the pertinent features of the technique comparison of the results obtained by the variational iteration method with those obtained by adomian decomposition method reveals that the first method is very effective and convenient the basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus

finding general and explicit solutions 2 1 dimensional broer kaup kupershmidt system nonlinear equation by exp function method abstract in this work we implement a relatively new analytical technique the exp function method for solving nonlinear special form of generalized nonlinear 2 1 dimensional broer kaup kupershmidt equation which may contain high nonlinear terms this method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations which applied in engineering mathematics some numerical examples are presented to illustrate the efficiency and reliability of exp method it is predicted that exp function method can be found widely applicable in engineering

approximate analytical solution for the zakharov kuznetsov equations with fully nonlinear dispersion in this paper variational iteration method vim is used to obtain numerical and analytical solutions for the zakharov kuznetsov equations with fully nonlinear dispersion comparisons with exact solution show that the vim is a powerful method for the solution of nonlinear equations

a variety of exact travelling wave solutions for the 2 1 dimensional boiti leon pempinelli equation abstract in this paper the 2 1 dimensional boiti leon pempinelli blp equation will be studied the tanh coth method will be used to obtain exact travelling wave solutions for this equation the exp function method will also be applied to the blp equation to derive a new variety of travelling wave solutions with distinct physical structures

numerical solutions of the nonlinear integro differential equations wavelet galerkin method and homotopy perturbation method this paper compares the homotopy perturbation method with the wavelet galerkin method for solving nonlinear integro differential equations from the computational viewpoint the homotopy perturbation method is more efficient and easy to use

optimal control based on the variational iteration method in this study an approach for designing an optimal control law based on the variational iteration method is proposed the idea consists of formulating the problem of optimal control under a variational problem form by substituting the control variable by its expression derived from the system model in the performance index then the solution of the variational problem obtained is achieved by satisfying the euler lagrange equation which is in general nonlinear therefore the variational iteration method is adopted to solve the euler lagrange equation obtained and the optimal control law is easily deduced by performing simple calculations to illustrate the suggested design approach a nonlinear system is considered and the result obtained is compared with the analytical solution to show the effectiveness of the proposed design approach

numerical resolution of an electromagnetic inverse medium problem at fixed frequency the aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency the governing equations are the time harmonic maxwell equations formulated in electric field in a two dimensional bounded domain we express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields our numerical reconstruction algorithm combines the bfgs method and an iterative process called the adaptive eigenspace inversion the unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator both the eigenspace and the mesh are iteratively adapted during the minimization procedure numerical experiments illustrate the performance of the reconstruction for various configurations

homotopy perturbation method for solving sixth order boundary value problems in this paper we apply the homotopy perturbation method for solving the sixth order boundary value problems by reformulating them as an equivalent system of integral equations this equivalent formulation is obtained by using a suitable transformation the analytical results of the integral equations have been obtained in terms of convergent series with easily computable components several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method comparisons are made to confirm the reliability of the homotopy perturbation method we have also considered an example where the homotopy perturbation method is not reliable

toward a modified variational iteration method the variational iteration method vim attracted much attention in the past few years as a promising method for solving nonlinear differential equations it is shown in this paper that the application of vim to a special kind of nonlinear differential equations leads to calculation of unneeded terms and more time consumed in repeated calculations for series solutions a modified vim is introduced to eliminate the shortcomings and its effectiveness is illustrated by some examples

on the solutions of nonlinear fractional klein gordon equation with modified riemann liouville derivative abstract in this paper fractional variational iteration method fvim is applied for finding approximate analytical solutions of nonlinear fractional klein gordon equation time fractional derivative is described in the riemann liouville sense a new application of fractional variational iteration method fvim is extended to derive analytical solutions in the form of a series for this equation the behavior of the solutions and the effects of different values of fractional order are indicated graphically it is shown that the solutions obtained by the fvim are reliable convenient and effective for strongly nonlinear partial equations with modified riemann liouville derivative

statistics of normally distributed initial imperfections abstract this paper offers a theoretical study on the probabilistic nature of critical loads buckling loads of structures subject to normally distributed initial imperfections explicit form of probability density function of critical loads are derived for various types of critical points double bifurcation points of structures with regular polygonal symmetry are dealt with by means of the group theoretic bifurcation theory the distribution of minimum values of the critical loads is investigated to present a statistical design index the theoretical and empirical probability density functions for simple structures are compared to show the validity and effectiveness of this method the method is quite efficient when it is directly applicable otherwise the explicit forms at least can greatly supplement the inefficiency of the conventional random method

a piecewise variational iteration method for riccati differential equations in this paper we introduce a piecewise variational iteration method for riccati differential equations which is a modified variational iteration method mvim the solutions of riccati differential equations obtained using the traditional variational iteration method vim give good approximations only in the neighborhood of the initial position however the solutions obtained using the mvim give good approximations for a larger interval rather than a local vicinity of the initial position some numerical examples are selected to illustrate the effectiveness and simplicity of the method numerical results show that the method does not share the drawback of the conventional vim and is a satisfactory method for riccati differential equations

periodic solutions for some strongly nonlinear oscillations by he s variational iteration method in this paper we implement a new analytical technique he s variational iteration method for some strongly nonlinear oscillations a correction functional is constructed by using a general lagrange multiplier which can be identified via the variational theory the obtained approximate solutions and periods are compared with exact or numerical results to verify the effectiveness and accuracy of the method

variational iteration method new development and applications variational iteration method has been favourably applied to various kinds of nonlinear problems the main property of the method is in its flexibility and ability to solve nonlinear equations accurately and conveniently in this paper recent trends and developments in the use of the method are reviewed major applications to nonlinear wave equation nonlinear fractional differential equations nonlinear oscillations and nonlinear problems arising in various engineering applications are surveyed the confluence of modern mathematics and symbol computation has posed a challenge to developing technologies capable of handling strongly nonlinear equations which cannot be successfully dealt with by classical methods variational iteration method is uniquely qualified to address this challenge the flexibility and adaptation provided by the method have made the method a strong candidate for approximate analytical solutions this paper outlines the basic conceptual framework of variational iteration technique with application to nonlinear problems both achievements and limitations are discussed with direct reference to approximate solutions for nonlinear equations a new iteration formulation is suggested to overcome the shortcoming a very useful formulation for determining approximately the period of a nonlinear oscillator is suggested examples are given to illustrate the solution procedure

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

exact solutions of nonlinear diffusion equations by variational iteration method in this paper he s variational iteration method is applied to obtain exact solutions of some nonlinear diffusion equations the variational iteration method is used to construct correction functionals using general lagrange multipliers identified optimally via the variational theory and the initial approximations can be freely chosen with unknown constants the solutions obtained are compared with those obtained by the adomian decomposition method and homotopy perturbation method showing excellent agreement but the variational iteration method is more effective he s variational iteration method can be introduced to overcome the difficulties arising in calculating adomian polynomials

numerical solution of a biological population model using he s variational iteration method this paper presents numerical solution of a degenerate parabolic equation arising in the spatial diffusion of biological populations the variational iteration method and adomian decomposition method are used for solving this equation and then numerical results are compared with each other showing that the variational iteration method leads to more accurate results furthermore variational iteration method overcomes the difficulty arising in calculating the adomian s polynomials which is an important advantage over the adomian decomposition method

application of the variational iteration method to the regularized long wave equation this paper applies the variational iteration method to the regularized long wave equation in this method a generalized lagrange multiplier is introduced to construct a correction functional for the discussed problem the multiplier can be identified optimally via variational theory three invariants of the motion are evaluated to determine the conservation properties of the system

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

application of a variational iteration method to linear and nonlinear viscoelastic models with fractional derivatives two nonlinear anelastic models with fractional derivatives describing the properties of a series of materials as polymers and polycrystalline materials are presented in this paper these models are studied analytically using a variational iteration method the paper clarifies the different ways in which the fractional differentiation operator can be defined a volterra series method of model parameters identification from the experimental data is also presented

exact solution of the heat equation with boundary condition of the fourth kind by he s variational iteration method in this paper solutions of the heat equation with the boundary condition of the fourth kind are presented the proposed solution is based on he s variational iteration method after the application of which the exact solution of the problem is obtained

numerical solution of a system of fourth order boundary value problems using variational iteration method abstract in this paper the variational iteration method is used to solve a system of fourth order boundary value problems associated with obstacle unilateral and contact problems numerical solution obtained by the method is of high accuracy moreover the higher order derivatives of numerical solution can also approximate the higher order derivatives of exact solution well five examples compared with those considered by siddiqi and akram s s siddiqi g akram numerical solution of a system of fourth order boundary value problems using cubic non polynomial spline method applied mathematics and computation 190 2007 652 661 show that the method is more efficient

variational iteration method for solving the epidemic model and the prey and predator problem in this article two problems are considered the first one is the problem of the spread of a non fatal disease in a population which is assumed to have constant size over the period of the epidemic and the other one is the problem of prey and predator the variational iteration method is employed to compute an approximation to the solutions of the systems of nonlinear ordinary differential equations governing on these problems the results are compared with the results obtained by adomian decomposition and power series methods some plots are presented to show the reliability and simplicity of the method

variational iteration method for solving a generalized pantograph equation the variational iteration method is applied to solve the generalized pantograph equation this technique provides a sequence of functions which converges to the exact solution of the problem and is based on the use of lagrange multipliers for identification of optimal value of a parameter in a functional employing this technique it is possible to find the exact solution or an approximate solution of the problem some examples are given to demonstrate the validity and applicability of the method and a comparison is made with existing results

finite symmetric systems and their analysis abstract symmetry of linear mechanical systems permits one to substantially reduce the effort in their analysis classification and structural analysis of the finite linear symmetric systems models are studied in this paper there are two variants of the symmetry approach mechanical and algebraic in accordance with the former a symmetric system is replaced by one or several small nonsymmetric subsystems which are subjected to special loads obtained from the initial set the total response of the original symmetric system is found by special superposition of partial responses of these subsystems the algebraic approach is based on the explicit block diagonal decomposition of the matrix equation corresponding to a symmetric system while both approaches have the same efficiency the latter is easier to implement and describe it is presented here the condtions under which the symmetry technique may be utilized do not include symmetry of the applied loads specifically symmetry of those loads which form the right side of the associated equations nevertheless if the loads are symmetric the efficiency of the symmetry approach substantially increases group theory which is widely used in this paper is the mathematical tool for the study of symmetry and all necessary notions are introduced

variational iteration method for solving nonlinear boundary value problems abstract in this paper he s variational iteration method is implemented to give approximate and analytical solutions for a class of boundary value problems the variational iteration method which produces the solutions in terms of convergent series requiring no linearization or small perturbation numerical examples are given and comparisons are made with the adomian decomposition method the fact that this method solves nonlinear equations without using adomian polynomials can be considered as an advantage of this method over adomian decomposition method

modified variational iteration method for boussinesq equation this paper applies the modified variational iteration method to solve a class of nonlinear partial differential equations boussinesq equation is used as a case study to illustrate the simplicity and effectiveness of the method comparison between variational iteration method and adomian decomposition method is made

variational iteration method for solving two point boundary value problems variational iteration method is introduced to solve two point boundary value problems numerical results demonstrate that the method is promising and may overcome the difficulty arising in adomian decomposition method

coupling technique of variational iteration and homotopy perturbation methods for nonlinear matrix differential equations the variational iteration method proposed by ji huan he is a new analytical method to solve nonlinear equations this paper applies the method to search for exact analytical solutions of linear differential equations with constant coefficients furthermore based on the precise integration method a coupling technique of the variational iteration method and homotopy perturbation method is proposed to solve nonlinear matrix differential equations a dynamic system and burgers equation are taken as examples to illustrate its effectiveness and convenience

a new technique for solving nonlinear integral differential equations in this paper the variational iteration method is used to solve a system of nonlinear integral differential equations this method is based on optimal identification of lagrange multipliers in the correction functionals numerical examples are given to show effectiveness convenience and accuracy of the method

derivation of the adomian decomposition method using the homotopy analysis method abstract adomian decomposition method has been used intensively to solve nonlinear boundary and initial value problems it has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits however very little has been done to address the mathematical foundation of the method and its error analysis in this article the mathematical derivation of the method using the homotopy analysis method is presented in addition an error analysis is addressed as well as the convergence criteria

variational iteration technique for solving higher order boundary value problems in this paper we have shown that higher order boundary value problems can be written as a system of integral equations which can be solved by using the variational iteration technique the analytical results of the equations have been obtained in terms of convergent series with easily computable components several examples are given to illustrate the efficiency and implementation of the method comparisons are made to confirm the reliability of the technique variational iteration technique may be considered as alternative and efficient for finding the approximate solutions of the boundary values problems

extension of the exp function method for systems of two dimensional burgers equations the exp function method has been applied to solve many functional equations so far but it has not been used for systems of equations directly in this paper the exp function method is applied to obtain generalized solitonary solutions of a system of two dimensional burgers equations stdbe it has been shown that the exp function method with the help of symbolic computation provides a very effective and powerful mathematical tool for solving a system of functional equations

a fractional variational iteration method for solving fractional nonlinear differential equations recently fractional differential equations have been investigated by employing the famous variational iteration method however all the previous works avoid the fractional order term and only handle it as a restricted variation a fractional variational iteration method was first proposed in g c wu e w m lee fractional variational iteration method and its application phys lett a 374 2010 2506 2509 and gave a generalized lagrange multiplier in this paper two fractional differential equations are approximately solved with the fractional variational iteration method

modified laplace variational iteration method for solving fourth order parabolic partial differential equation with variable coefficients abstract in the present study a new amendment in laplace variational iteration method for the solution of fourth order parabolic partial differential equations with variable coefficients is revealed i e modified laplace variational iteration method ml vim the proposed modification is made by coupling of two methods one of them is variational iteration method vim and the other one is laplace transformation lt our modification has an important beauty that one has no need to compute lagrange multiplier via integration nor by taking convolution theorem and has a simple way to use in the implementation of our proposed scheme moreover homotopy perturbation method hpm with he s polynomials is employed for the computation of nonlinear terms the main improvement of our proposed scheme is the reduction of the problem to a simple one which also embraces for solving a nonlinear term some illustrated examples are interpreted which unveil the robustness and accuracy of the newly developed scheme

variational iteration method for twelfth order boundary value problems in this paper he s variational iteration method is applied to solve twelfth order boundary value problems the numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the variational iteration method is of high accuracy more convenient and efficient for solving high order boundary value problems

bifurcation hierarchy of symmetric structures abstract a group theoretic method for the analysis of bifurcation behavior of regular polygonal symmetric structures is described possible bifurcation paths and points of these structures are categorized in terms of dihedral and cyclic groups which express the symmetry in particular we offer a complete description of those double bifurcation points which occur due to group symmetry the type the number and the stability of bifurcation paths branching at these points are determined by deriving bifurcation equations the existence of a potential function plays a substantial role for the existence of bifurcation paths as a result of these all possible bifurcation process can be known a priori as a natural consequence of bifurcation hierarchy before actual numerical analysis an implementation of this method in numerical analysis shows its validity and usability

the adomian decomposition method in turning point problems in this paper the decomposition method is applied to boundary value problems of ordinary differential equations with a parameter exhibiting turning points

the numerical simulation for stiff systems of ordinary differential equations in this paper the variational iteration method is applied to solve systems of ordinary differential equations in both linear and nonlinear cases focusing interest on stiff problems some examples are given to illustrate the accuracy and effectiveness of the method we compare our results with results obtained by the adomian decomposition method this comparison reveals that the variational iteration method is easier to be implemented in fact the variational iteration method is a promising method to various systems of linear and nonlinear equations

the variational iteration method for solving a neutral functional differential equation with proportional delays in this paper the variational iteration method is applied to neutral functional differential equations with proportional delays illustrative examples are given to show the efficiency of the method we also compare the performance of the method with that of a particular runge kutta method and a one leg q method

a generalized g g expansion method and its application to the 2 1 dimensional broer kaup equations abstract in this paper a generalized g g expansion method is used to seek more general exact solutions of the 2 1 dimensional broer kaup equations as a result non travelling wave solutions with three arbitrary functions are obtained including hyperbolic function solutions trigonometric function solutions and rational solutions the proposed method is more powerful than wang et al s method in m l wang x z li j l zhang the g g expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics phys lett a 372 2008 417 423 and it can be used for many other nonlinear evolution equations in mathematical physics

constructing of exact solutions to the kdv and burgers equations with power law nonlinearity by the extended g g expansion method abstract the extended g g expansion method is introduced to construct more general exact traveling wave solutions to the kdv and burgers equations with any order nonlinear terms the traveling wave solutions are expressed by the hyperbolic functions the trigonometric functions and the rational functions when the parameters take up special values new solitary periodic and complex solutions are also derived from the traveling wave solutions

analytical solution of a fractional diffusion equation by variational iteration method in the present paper the analytical approximate solution of a fractional diffusion equation is deduced with the help of powerful variational iteration method by using an initial value the explicit solutions of the equation for different cases have been derived which accelerate the rapid convergence of the series solution the present method performs extremely well in terms of efficiency and simplicity numerical results for different particular cases of the problem are presented graphically

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

variational iteration method for nonlinear age structured population models this paper investigates nonlinear age structured population models the numerical solutions are obtained by using the variational iteration method and are of high accuracy two numerical examples are presented to illustrate the strength of the method

critical initial imperfection of structures abstract a method is introduced for determining the critical initial imperfection of discretized structures that decreases the load bearing capacity most rapidly the effects of imperfections on simple critical points such as limit points of loads and simple bifurcation points are theoretically investigated based on the idea of the lyapunov schmidt decomposition developed in bifurcation theory imperfection sensitivity varies with the types of points nonetheless critical imperfection pattern is expressed in the same formula regardless of the types among various imperfections the most influential can be found in a quantitative manner the validity and the usability of the proposed method are illustrated through its application to simple example structures

application of the extended homotopy perturbation method to a kind of nonlinear evolution equations based on the homotopy perturbation method we propose a new extended homotopy perturbation method we apply the method to solve a kind of nonlinear evolution equations with the help of the symbolic computation system maple the success of the paper lies on the fact that we do not conform to the traditional homotopy mode but construct a new homotopy of the given equations the results reveal that we can obtain the approximation solution of a kind of nonlinear evolution equations

variational iteration method for unsteady flow of gas through a porous medium using he s polynomials and pade approximants in this paper we apply the variational iteration method using he s polynomials for finding the analytical solution of unsteady flow of gas through a porous medium the proposed method is an elegant combination of he s variational iteration and the homotopy perturbation methods the suggested algorithm is quite efficient and is practically well suited for use in such problems the proposed iterative scheme finds the solution without any discretization linearization or restrictive assumptions the diagonal pade approximants are effectively used in the analysis to capture the essential behavior of the solution and to determine the initial slope a clear advantage of this technique over the decomposition method is that no calculation of adomian s polynomials is needed

variational iteration method for solving cubic nonlinear schrodinger equation the variational iteration method is applied to solve the cubic nonlinear schrodinger cnls equation in one and two space variables in both cases we will reduce the cnls equation to a coupled system of nonlinear equations numerical experiments are made to verify the efficiency of the method comparison with the theoretical solution shows that the variational iteration method is of high accuracy

comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations in this article the homotopy perturbation method proposed by j h he is adopted for solving linear fractional partial differential equations the fractional derivatives are described in the caputo sense comparison of the results obtained by the homotopy perturbation method with those obtained by the variational iteration method reveals that the present methods are very effective and convenient

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

critical imperfection of symmetric structures a method is presented to determine the critical most unfavorable initial imperfection of structures of regular polygonal symmetry denoted by dihedral groups a critical point of such structures is either simple or forced to be double by the symmetry and the group representation theory is employed to deal with the degeneracy due to symmetry the method is developed further to incorporate the symmetry of imperfections in many cases of practical interest the critical imperfection is given explicitly as the product of imperfection sensitivity matrix and the critical eigenvector it is shown that the symmetry in the critical eigenvectors of the tangent stiffness matrix is inherited to the symmetry in the critical imperfection mode

application of he s methods to nonlinear chemistry problems in this paper he s variational iteration method vim and homotopy perturbation method hpm are implemented for solving analytically two systems of ordinary differential equations that often appear in chemical applications in both methods the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions the solution procedure is of utter simplicity and the obtained solution is of high accuracy

numerical solutions of nonlinear evolution equations using variational iteration method the variational iteration method is used to solve three kinds of nonlinear partial differential equations coupled nonlinear reaction diffusion equations hirota satsuma coupled kdv system and drinefel d sokolov wilson equations numerical solutions obtained by the variational iteration method are compared with the exact solutions revealing that the obtained solutions are of high accuracy he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomial in adomian method the method is straightforward and concise and it can also be applied to other nonlinear evolution equations in mathematical physics

fourth order integro differential equations using variational iteration method in this paper the variational iteration method proposed by ji huan he is applied to solve both linear and nonlinear boundary value problems for fourth order integro differential equations the numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the variational iteration method is of high accuracy more convenient and efficient for solving integro differential equations

approximate solution of nonlinear differential equations with convolution product nonlinearities in this paper a new iteration method is proposed to solve nonlinear problems special attention is paid to nonlinear differential equations with convolution product nonlinearities the results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems furthermore the first order of approximations are more accurate than perturbation solutions at high order of approximation