a fast fourier transform on multipoles fftm algorithm for solving helmholtz equation in acoustics analysis this article presents a fast algorithm for the efficient solution of the helmholtz equation the method is based on the translation theory of the multipole expansions here the speedup comes from the convolution nature of the translation operators which can be evaluated rapidly using fast fourier transform algorithms also the computations of the translation operators are accelerated by using the recursive formulas developed recently by gumerov and duraiswami siam j sci comput 25 1344 1381 2003 it is demonstrated that the algorithm can produce good accuracy with a relatively low order of expansion efficiency analyses of the algorithm reveal that it has computational complexities of o na where a ranges from 1 05 to 1 24 however this method requires substantially more memory to store the translation operators as compared to the fast multipole method hence despite its simplicity in implementation this memory requirement issue may limit the application of this algorithm to solving very lar

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

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

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

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

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

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

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

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

acoustic scattering by arbitrary distributions of disjoint homogeneous cylinders or spheres a t matrix formulation is presented to compute acoustic scattering from arbitrary disjoint distributions of cylinders or spheres each with arbitrary uniform acoustic properties the generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers by employing field expansions based on orthogonal harmonic functions continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal analytic expressions to eliminate the need for integral equations the effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant numerical results establish the validity and efficiency of the outer iteration procedure for nested objects two and three dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two dimensional approximations to three dimensional scattering of elevation focused beams

a spectral element approach for the stability of delay systems we describe a spectral element approach to study the stability and equilibria solutions of delay differential equations ddes in contrast to the prototypical temporal finite element analysis tfea the described spectral element approach admits spectral rates of convergence and allows exploiting hp convergence schemes the described approach also avoids the limitations of analytical integrations in tfea by using highly accurate numerical quadratures enabling the study of more complicated ddes the effectiveness of this new approach is compared with well established methods in the literature using various case studies specifically the stability results are compared with the conventional tfea and legendre collocation methods whereas the equilibria solutions are compared with the numerical simulations and the homotopy perturbation method hpm solutions our results reveal that the presented approach can have higher rates of convergence than both collocation methods and the hpm copyright 2011 john wiley sons ltd

calculation of acoustical scattering from a cluster of scatterers the problem of determining the field scattered by a cluster of scatterers when they are insonified by a known acoustical field is addressed the problem is formulated by using the t matrix method and the resulting system of linear equations is solved by using the multilevel fast multipole algorithm mlfma and the fast multipole method fast fourier transform fmmfft method and the efficiency of the two methods is compared it was observed that in general the mlfma performs better than the fmmfft algorithm however when the scatterers are distributed uniformly on a rectangular grid the fmmfft algorithm performs as good as the mlfma the accuracy of the methods is evaluated by modeling a spherical scatterer as composed of many small spheres

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

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

the fast multipole method we study integral methods applied to the resolution of the maxwell equations where the linear system is solved using an iterative method which requires only matrix vector products the fast multipole method fmm is one of the most efficient methods used to perform matrix vector products and accelerate the resolution of the linear system a problem involving n degrees of freedom may be solved in cniternlogn floating operations where c is a constant depending on the implementation of the method in this article several techniques allowing one to reduce the constant c are analyzed this reduction implies a lower total cpu time and a larger range of application of the fmm in particular new interpolation and anterpolation schemes are proposed which greatly improve on previous algorithms several numerical tests are also described these confirm the efficiency and the theoretical complexity of the fmm

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

solving nonlinear partial differential equations using the modified variational iteration pade technique in this paper the modified variational iteration method mvim is reintroduced with the enhancement of pade approximants to lengthen the interval of convergence of vim or mvim when used alone in solving nonlinear problems kdv mkdv burger s and lax s equations are used as examples to illustrate the effectiveness and convenience of the proposed technique

computation of scattering from clusters of spheres using the fast multipole method a t matrix based method of solution of the multiple scattering problem was presented by the authors j acoust soc am 112 2688 2701 2002 this method can be applied to the computation of relatively small problems since the number of operations required grows with the number of spheres n as o n3 and with the sixth power of the wave number the use of iterative techniques accelerated using the fast multipole method fmm can accelerate this solution as presented by koc and chew j acoust soc am 103 721 734 1998 originally in this study we present a method that combines preconditioned krylov subspace iterative techniques fmm accelerated matrix vector products a novel fmm based preconditioner and fast translation techniques that enable us to achieve an overall algorithm in which the cost of the matrix vector multiplication grows with n as o n logn and with the third power of the wave number we discuss the convergence of the iterative techniques selection of the truncation number errors in the solution and other issues the results of the solution of test problems obtained with the method for n approximately 10 2 10 4 for different wave numbers are presented

recursions for the computation of multipole translation and rotation coefficients for the 3 d helmholtz equation we develop exact expressions for the coefficients of series representations of translations and rotations of local and multipole fundamental solutions of the helmholtz equation in spherical coordinates these expressions are based on the derivation of recurrence relations some of which to our knowledge are presented here for the first time the symmetry and other properties of the coefficients are also examined and based on these efficient procedures for calculating them are presented our expressions are direct and do not use the clebsch gordan coefficients or the wigner 3 j symbols although we compare our results with methods that use these to prove their accuracy for evaluating an nt term truncation of the translated series involving o n t 2 multipoles our expressions require o n t 3 evaluations compared to previous exact expressions that require o n t 5 operations

a fast high order algorithm for multiple scattering from large sound hard three dimensional configurations abstract we describe an efficient fast high order algorithm for simulating acoustic scattering in an unbounded three dimensional medium exterior to a configuration with a large number of sound hard particles surface integral representations of the scattered and far fields facilitate reformulation of the model for unknown fields on the closed bounded surface of each particle in the configuration our surface integral equation based algorithm uses a multiple scattering variant of complex dense system krylov subspace techniques combined with an efficient matrix vector product scheme in this article we develop a memory efficient fast algorithm in three steps using appropriate expansion methods em the first step is based on a radiating basis em radbem and the third step is based on a regular basis em regbem the second step transforms radbem to regbem and is accelerated using the well known multilevel fast multipole method the full algorithm has linear complexity with respect to the number of particles to evaluate quadratically large multiple scattering interactions exterior to the configuration we present numerical results obtained with our fast algorithm for simulations with up to about twenty thousand sound hard particles and for large dense complex systems with more than twelve million unknowns we compare our results with a recent high order accurate accelerated direct solver by bremer et al 2015 and demonstrate substantial computational advantages of our radbem regbem algorithm

application of he s variational iteration method to nonlinear jaulent miodek equations and comparing it with adm instead of finding a small parameter for solving nonlinear problems through perturbation method a new analytical method called he s variational iteration method vim is introduced to be applied to solve nonlinear jaulent miodek coupled kdv and coupled mkdv equations in this article in this method general lagrange multipliers are introduced to construct correction functionals for the problems the multipliers can be identified optimally via the variational theory the results are compared with exact solutions

the fast multipole method i error analysis and asymptotic complexity this paper is concerned with the application of the fast multipole method fmm to the maxwell equations this application differs in many aspects from other applications such as the n body problem laplace equation and quantum chemistry etc the fmm leads to a significant speed up in cpu time with a major reduction in the amount of computer memory needed when performing matrix vector products this leads to faster resolution of scattering of harmonic plane waves from perfectly conducting obstacles emphasis here is on a rigorous mathematical approach to the problem we focus on the estimation of the error introduced by the fmm and a rigorous analysis of the complexity o n log n of the algorithm we show that error estimates reported previously are not entirely satisfactory and provide sharper and more precise estimates

efficient numerical solution of acoustic scattering from doubly periodic arrays of axisymmetric objects we present a high order accurate boundary based solver for three dimensional 3d frequency domain scattering from a doubly periodic grating of smooth axisymmetric sound hard or transmission obstacles we build the one obstacle solution operator using separation into p azimuthal modes via the fft the method of fundamental solutions with n proxy points lying on a curve and dense direct least squares solves the effort is o n 3 p with a small constant periodizing then combines fast multipole summation of nearest neighbors with an auxiliary global helmholtz basis expansion to represent the distant contributions and enforcing quasiperiodicity and radiation conditions on the unit cell walls eliminating the auxiliary coefficients and preconditioning with the one obstacle solution operator leaves a well conditioned square linear system that is solved iteratively the solution time per incident wave is then o n p at fixed frequency our scheme avoids singular quadratures periodic green s functions and lattice sums and its convergence rate is unaffected by resonances within obstacles we include numerical examples such as scattering from a grating of period 13 13 comprising highly resonant sound hard cups each needing n p 64800 surface unknowns to 10 digit accuracy in half an hour on a desktop

a method to compute the radiated sound power based on mapped acoustic radiation modes application of modal expansion approach for the exterior acoustic field has drawn wide research interests in recent years this is primarily due to the acoustic radiation modes arm that can diagonalize the impedance matrix hence significantly simplifying the computation of radiated sound power the orthogonal arm are typically calculated via a standard eigenvalue analysis of the impedance matrix which normally leads to numerical difficulties especially for wideband frequency and large scale problems in this paper a theory of mapped arm is proposed to avoid the cumbersome computation of arm for convex structures a mapping relationship between the arm on the surface of an equivalent spherical source and the mapped arm on the surface of a convex structure is obtained based on the equivalent source method multipole expansion method and boundary integral method furthermore analytical expressions for the radiated sound power of structures vibrating in its mapped arm as well as that of spheres are derived finally a simple method is proposed to approximate the radiated sound power based on the modal decomposition method and the mapping relationship numerical simulations are conducted to validate the accuracy and efficiency of the proposed approach and different vibrating structures with various geometries are considered results demonstrate that the proposed methodology for calculating the radiated sound power of convex structures is very efficient and accurate as compared with the traditional approach

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

multiple scattering by multiple spheres a new proof of the lloyd berry formula for the effective wavenumber we provide the first classical derivation of the lloyd berry formula for the effective wavenumber of an acoustic medium filled with a sparse random array of identical small scatterers our approach clarifies the assumptions under which the lloyd berry formula is valid more precisely we derive an expression for the effective wavenumber which assumes the validity of lax s quasi crystalline approximation but makes no further assumptions about scatterer size and then we show that the lloyd berry formula is obtained in the limit as the scatterer size tends to zero

a scalar potential formulation and translation theory for the time harmonic maxwell equations we develop a computational method based on the debye scalar potential representation which efficiently reduces the solution of maxwell s equations to the solution of two scalar helmholtz equations one of the key contributions of this paper is a theory for the translation of maxwell solutions using such a representation since the scalar potential form is not invariant with respect to translations the translation theory is developed by introducing conversion operators which enable the representation of the electric and magnetic vector fields via scalar potentials in an arbitrary reference frame advantages of this representation include the fact that only two helmholtz equations need be solved and moreover the divergence free constraints are satisfied automatically by construction truncation error bounds are also presented the availability of a translation theory and error bounds for this representation can find application in methods such as the fast multipole method for illustration of the use of the representation and translation theory we implemented an algorithm for the simulation of mie scattering off a system of spherical objects of different sizes and dielectric properties using a variant of the t matrix method the resulting system was solved using an iterative method based on gmres the results of the computations agree well with previous computational and experimental results

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

numerical approach to differential equations of fractional order in this paper the variational iteration method and the adomian decomposition method are implemented to give approximate solutions for linear and nonlinear systems of differential equations of fractional order the two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations in these schemes the solution takes the form of a convergent series with easily computable components this paper presents a numerical comparison between the two methods for solving systems of fractional differential equations numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order

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

three dimensional acoustic scattering by multiple spheres using collocation multipole method abstract this paper presents a semi analytical approach to solve the three dimensional acoustic scattering problems with multiple spheres subjected to a plane sound wave to satisfy the three dimensional helmholtz equation in a spherical coordinate system the multipole expansion for the scattered acoustic field is formulated in terms of the associated legendre functions and the spherical hankel functions that also satisfy the radiation condition at infinity the multipole method the directional derivative and the collocation technique are combined to propose a collocation multipole method in which the acoustic field and its normal derivative with respect to the non local spherical coordinate system can be calculated without any truncated error frequently occurred when using the addition theorem the boundary conditions are satisfied by collocating points on the surface of each sphere by truncating the higher order terms of the multipole expansion a finite linear algebraic system is acquired the scattered field can then be determined according to the given incident sound wave the convergence analysis considering the specified error the separation of spheres and the wave number of an incident wave is first carried out to provide guide lines for the proposed method then the proposed results for acoustic scattering by one two and three spheres are validated by using the available analytical method and numerical methods such as boundary element method finally the effects of the separation between scatterers the incident wave number and the incident angle on the acoustic scattering are investigated extensively

a wiener wintner theorem for 1 f power spectra abstract wiener s generalized harmonic analysis gha provides a theory of harmonic analysis for subspaces of tempered functions not accessible to the l 1 l 2 and fourier series theories and it does it in a way that is usually more quantitative than that provided by the theory of distributions on the other hand gha does not yield an adequate spectral analysis of large classes of functions including nonstationary processes and in particular 1 f noise in this paper we adapt gha to deal with 1 f noise by extending the wiener wintner theorem to the case of 1 f power spectra

variational iteration method some recent results and new interpretations this paper is an elementary introduction to the concepts of variational iteration method first the main concepts in variational iteration method such as general lagrange multiplier restricted variation correction functional are explained heuristically subsequently the solution procedure is systematically addressed in particular for nonlinear oscillators particular attention is paid throughout the paper to give an intuitive grasp for the method the main motivation is to put things together in a convenient form for later reference and systematic use

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

document reranking by term distribution and maximal marginal relevance for chinese information retrieval in this paper we propose a document reranking method for chinese information retrieval the method is based on a term weighting scheme which integrates local and global distribution of terms as well as document frequency document positions and term length the weight scheme allows randomly setting a larger portion of the retrieved documents as relevance feedback and lifts off the worry that very fewer relevant documents appear in top retrieved documents it also helps to improve the performance of maximal marginal relevance mmr in document reranking the method was evaluated by map mean average precision a recall oriented measure significance tests showed that our method can get significant improvement against standard baselines and outperform relevant methods consistently

error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem the numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate but fast methods such as the fast multipole method however since these methods are only approximate it is important to have an estimate for the error introduced in such calculations an analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtained the error caused by polynomial interpolation in a multilevel fast multipole algorithm is also analyzed the total error introduced in a multilevel implementation is also investigated numerically

a mesh free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators a multiple scattering approach is presented to compute the solution of the helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere the solution is represented in terms of partial wave expansions and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces this approach yields high order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable numerical results are presented to demonstrate the accuracy and efficiency of the method

a broadband fast multipole accelerated boundary element method for the three dimensional helmholtz equation the development of a fast multipole method fmm accelerated iterative solution of the boundary element method bem for the helmholtz equations in three dimensions is described the fmm for the helmholtz equation is significantly different for problems with low and high kd where k is the wavenumber and d the domain size and for large problems the method must be switched between levels of the hierarchy the bem requires several approximate computations numerical quadrature approximations of the boundary shapes using elements and these errors must be balanced against approximations introduced by the fmm and the convergence criterion for iterative solution these different errors must all be chosen in a way that on the one hand excess work is not done and on the other that the error achieved by the overall computation is acceptable details of translation operators for low and high kd choice of representations and bem quadrature schemes all consistent with these approximations are described

new applications of variational iteration method abstract the variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled schrodinger kdv generalized kdv and shallow water equations the exact and numerical solutions obtained by variational iteration method are compared with that obtained using adomian decomposition method the comparison shows that the two solutions obtained are excellent agreement the method is made showing that the former is more effective than the latter in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

adomian decomposition method for solving bvps for fourth order integro differential equations the adomian decomposition method adm is applied to solve both linear and nonlinear boundary value problems bvps for fourth order integro differential equations the numerical results obtained with minimum amount of computation or mathematics compare reasonably well with exact solutions

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

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

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

a new application of he s variational iteration method for quadratic riccati differential equation by using adomian s polynomials in this paper the quadratic riccati differential equation is solved by he s variational iteration method with considering adomian s polynomials comparisons were made between adomian s decomposition method adm homotopy perturbation method hpm and the exact solution in this application we do not have secular terms and if l lagrange multiplier is equal 1 then the adomian s decomposition method is obtained the results reveal that the proposed method is very effective and simple and can be applied for other nonlinear problems

an analytical approach to the dynamic analysis of a rotating electric machine this study presents an analytical approach to the dynamic problem encountered by a rotating electric machine supported by nonlinear bearings with damping properties subjected to a forcing excitation caused by an unbalanced force and a parametric excitation caused by an axial thrust the method employed in this analytical study is the optimal variational iteration method ovim which proves to be very effective and accurate in solving nonlinear problems the results are presented in the form of a time displacement response the results obtained from numerical simulations are in very good agreement with the approximate analytical results obtained through the proposed method

semi analytical computation of laplacian green functions in three dimensional domains with disconnected spherical boundaries abstract the generalized method of separation of variables gmsv is applied to solve boundary value problems for the laplace operator in three dimensional domains with disconnected spherical boundaries e g an arbitrary configuration of non overlapping partially reactive spherical sinks or obstacles we consider both exterior and interior problems and all most common boundary conditions dirichlet neumann robin and conjugate one using the translational addition theorems for solid harmonics to switch between the local spherical coordinates we obtain a semi analytical expression of the green function as a linear combination of partial solutions whose coefficients are fixed by boundary conditions although the numerical computation of the coefficients involves series truncation and solution of a system of linear algebraic equations the use of the solid harmonics as basis functions naturally adapted to the intrinsic symmetries of the problem makes the gmsv particularly efficient especially for exterior problems the obtained green function is the key ingredient to solve boundary value problems and to determine various characteristics of stationary diffusion such as reaction rate escape probability harmonic measure residence time and mean first passage time to name but a few the relevant aspects of the numerical implementation and potential applications in chemical physics heat transfer electrostatics and hydrodynamics are discussed

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

application of homotopy perturbation and variational iteration methods to nonlinear heat transfer and porous media equations perturbation methods depend on a small parameter which is difficult to be found for real life nonlinear problems to overcome this shortcoming two new but powerful analytical methods are introduced to solve nonlinear heat transfer problems in this article one is he s variational iteration method vim and the other is the homotopy perturbation method hpm the vim is 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 hpm deforms a difficult problem into a simple problem which can be easily solved nonlinear convective radiative cooling equation nonlinear heat equation porous media equation and nonlinear heat equation with cubic nonlinearity are used as examples to illustrate the simple solution procedures comparison of the applied methods with exact solutions reveals that both methods are tremendously effective

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

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