advances in the adomian decomposition method for solving two point nonlinear boundary value problems with neumann boundary conditions a new straightforward approach for solving ordinary and partial second order boundary value problems with neumann boundary conditions is introduced in this research this approach depends mainly on the adomian decomposition method with a new definition of the differential operator and its inverse which has been modified for neumann boundary conditions the effectiveness of the proposed approach is verified by several linear and nonlinear examples

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

spectral methods based on new formulations for coupled stokes and darcy equations in this paper we consider the numerical solution of the stokes and darcy coupled equations which frequently appears in porous media modeling the main contribution of this work is as follows first we introduce a new formulation for the stokes darcy coupled equations subject respectively to the beavers joseph saffman interface condition and an alternative matching interface condition secondly we prove the well posedness of these weak problems by using the classical saddle point theory thirdly some spectral approximations to the weak problems are proposed and analyzed and some error estimates are provided it is found that the new formulations significantly simplify the error analysis and numerical implementation finally some two dimensional spectral and spectral element numerical examples are provided to demonstrate the efficiency of our methods

an algorithm for solving boundary value problems in this paper a numerical algorithm based on the decomposition technique is presented for solving a class of nonlinear boundary value problems the method is implemented for well known examples including troesch s and bratu s problems which have been extensively studied the scheme is shown to be highly accurate and only a few terms are required to obtain accurate computable solutions

numerical solution of functional integral equations by the variational iteration method in the present article we apply the variational iteration method to obtain the numerical solution of the functional integral equations this method does not need to be dependent on linearization weak nonlinearity assumptions or perturbation theory application of this method in finding the approximate solution of some examples confirms its validity the results seem to show that the method is very effective and convenient for solving such equations

a novel method for nonlinear two point boundary value problems combination of adm and rkm abstract in this paper a novel method is proposed for solving nonlinear two point boundary value problems bvps this method is based on a combination of the adomian decomposition method adm and the reproducing kernel method rkm a major advantage of this method over standard adm is that it can avoid unnecessary computation in determining the unknown parameters the proposed method can be applied to singular and nonsingular bvps numerical results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for solving nonlinear two point boundary value problems

cubulating graphs of free groups with cyclic edge groups we prove that if g is a group that splits as a finite graph of finitely generated free groups with cyclic edge groups and g has no non euclidean baumslag solitar subgroups then g is the fundamental group of a compact nonpositively curved cube complex in addition if g is also word hyperbolic i e if g contains no baumslag solitar subgroups of any type we show that g is linear in fact is a subgroup of sl n z

solving two point boundary value problems using combined homotopy perturbation method and green s function method in this paper an algorithm is proposed for the solution of second order boundary value problems with two point boundary conditions the green s function method is applied first to transform the ordinary differential equation into an equivalent integral one which has already satisfied the boundary conditions and then the homotopy perturbation method is used to the resulting equation to construct the numerical solution for such problems numerical examples demonstrate the efficiency and reliability of the algorithm developed it is quite accurate and readily implemented for both linear and nonlinear differential equations with homogeneous and nonhomogeneous boundary conditions furthermore the lower order approximation is of higher accuracy for most cases some other extended applications of this algorithm are also exhibited

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

pseudospectral least squares method for stokes darcy equations we investigate the first order system least squares legendre and chebyshev pseudospectral method for coupled stokes darcy equations a least squares functional is defined by summing up the weighted l 2 norm of residuals of the first order system for coupled stokes darcy equations and that of beavers joseph saffman interface conditions continuous and discrete homogeneous functionals are shown to be equivalent to a combination of weighted h div and h 1 norms for stokes and darcy equations the spectral convergence for the legendre and chebyshev methods is derived some numerical experiments are demonstrated to validate our analysis

a parallel domain decomposition method for coupling of surface and groundwater flows abstract in this paper we construct a robust parallel method based on a recently developed non overlapping domain decomposition methodology to accurately model natural coupling of surface and groundwater flows stokes and darcy equations are formulated and solved within the surface and subsurface regions respectively a new type of robin robin boundary condition is proposed on the common boundary for the coupling of those systems the formulation provides great flexibility for multi physics coupling and is suitable for efficient parallel implementation meanwhile it is stable with inherent system parameter variation a numerical example is provided to verify the theory

irreducible affine varieties over a free group i irreducibility of quadratic equations and nullstellensatz the object of this paper which consists of two parts is to describe irreducible varieties over free groups and to characterize finitely generated fully residually free groups we prove that any variety over a free group f can be defined by a finite number of systems of equations s 1 in triangular form where quadratic words play the role of leading terms algebraically irreducible varieties are exactly the varieties whose coordinate groups are fully residually f the crucial point of the classification of fully residually free groups is to prove that the coordinate groups of irreducible varieties are embeddable into lyndon s free z x group f since every finitely generated fully residually free group is a free factor of the coordinate group of an irreducible variety and the group f is fully residually f we obtain a characterization of finitely generated fully residually free groups as subgroups of f the group f and its subgroups have been studied extensively during the last several years in particular every finitely generated subgroup of f hence every finitely generated fully residually free group can be obtained from free abelian groups of finite rank by finitely many free products with amalgamation and hnn extensions of the type where amalgamated and associated subgroups are free abelian of finite rank in particular this implies that every finitely generated fully residually free group is finitely presented there are three parts to this paper algebraic geometry over free groups the theory of free exponential groups and makanin razborov s machinery to deal with equations over free groups 11 14 13 the algebraic geometry approach has been shown to be very usefull in dealing with equations over groups it provides necessary topological means and a method to transcribe geometric notions into pure group theoretic language following baumslag myasnikov remeslennikov 1 we use the standard algebraic geometry notions such as variety zariski topology irreducibility of varieties radicals and coordinate groups some of the ideas of the algebraic geometry approach go back to r lyndon 9 e rips j stallings 16

a variational iteration method for solving troesch s problem troesch s problem is an inherently unstable two point boundary value problem a new and efficient algorithm based on the variational iteration method and variable transformation is proposed to solve troesch s problem the underlying idea of the method is to convert the hyperbolic type nonlinearity in the problem into polynomial type nonlinearities by variable transformation and the variational iteration method is then directly used to solve this transformed problem only the second order iterative solution is required to provide a highly accurate analytical solution as compared with those obtained by other analytical and numerical methods

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

a new application of he s variational iteration method for the solution of the one phase stefan problem in this paper we will use the variational iteration method to find an approximate solution of a one phase stefan problem this problem consists in finding the distribution of temperature in the domain and the position of a moving interface the problem under consideration is at first approximated with a system of differential equations in a domain with known boundary and next the system constructed in this way is solved by the variational iteration method the validity of the approach is verified by comparing the results obtained with an analytical solution

irreducible affine varieties over a free group ii systems in triangular quasi quadratic form and description of residually free groups abstract we shall prove the conjecture of myasnikov and remeslennikov 4 which states that a finitely generated group is fully residually free every finite set of nontrivial elements has nontrivial images under some homomorphism into a free group if and only if it is embeddable in the lyndon s exponential groupfz x which is thez x completion of the free group herez x is the ring of polynomials of one variable with integer coefficients historically lyndon s attempts to solve tarski s famous problem concerning the elementary equivalence of free groups of different ranks led him to introducefz x an free group is a groupgsuch that the class of formulas true ing is the same as the class of formulas true in a nonabelian free group a finitely generated group is free if and only if it is fully residually free 22 our result gives an algebraic description of free groups we shall give an algorithm to represent a solution set of an arbitrary system of equations overfas a union of finite number of irreducible components in the zariski topology onfn the solution set for every system is contained in the solution set of a finite number of systems in triangular form with quadratic words as leading terms the possibility of such a decomposition for a solution set was conjectured by razborov in 20 and also by rips we shall give a description of systems of equations determining irreducible components using methods developed in 13 19 it is possible to find some of these methods in 18 we are thankful to e rips for attracting our attention to these techniques

the steady temperature distributions with different types of nonlinearities the nonlinear two point boundary value problems are solved and the steady temperature distributions in a rod are found by considering different types of the nonlinear parts of the problems particularly in the polynomial exponential and trigonometric forms in this paper with the aid of some transformations the variational iteration method s scheme is reproduced for the nonlinear problems including two point boundary value problems the illustrative related problems are solved by means of the method scheme

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

variational iteration method for sturm liouville differential equations in this article he s variational iteration method is applied to linear sturm liouville eigenvalue and boundary value problems including the harmonic oscillator in this method solutions of the problems are approximated by a set of functions that may include possible constants to be determined from the boundary conditions by computing variations the lagrange multipliers are derived and the generalised expressions of variational iterations are constructed numerical results show that the method is simple however powerful and effective

cubulating malnormal amalgams let g be a group splitting as a graph of groups where each vertex group acts properly on a cat 0 cube complex when g is hyperbolic relative to virtually abelian subgroups we examine conditions producing a proper action of g on a cat 0 cube complex when g is hyperbolic this action is also cocompact

cubulating hyperbolic free by cyclic groups the irreducible case let v be a nite graph and let v v be an irreducible train track map whose mapping torus has word hyperbolic fundamental group g then g acts freely and cocompactly on a cat 0 cube complex hence if f is a nite rank free group and f f an irreducible monomorphism so that g f is word hyperbolic then g acts freely and cocompactly on a cat 0 cube complex this holds in particular if is an irreducible automorphism with g f o z word hyperbolic

numerical solution of troesch s problem by simple shooting method this paper describes a simple and efficient approach to the troesch s problem in this approach the hyperbolic nonlinear term in the equation is first converted into polynomial nonlinear terms by variable transformation and a simple shooting method is then used directly to solve this transformed problem the calculated results are in excellent agreement with those obtained by other analytical and numerical methods

approximation of coupled stokes darcy flow in an axisymmetric domain abstract in this article we investigate the numerical approximation of coupled stokes and darcy fluid flow equations in an axisymmetric domain the fluid flow is assumed to be axisymmetric rewriting the problem in cylindrical coordinates reduces the 3 d problem to a problem in 2 d this reduction to 2 d requires the numerical analysis to be studied in suitably weighted hilbert spaces in this setting we show that the proposed approximation scheme has a unique solution and derive corresponding a priori error estimate computations for an example with a know solution are presented which support the a priori error estimate computations are also given for a model of fluid flow in the eye

adaptive partitioned methods for the time accurate approximation of the evolutionary stokes darcy system abstract this paper develops analyzes and tests a time accurate partitioned method for the stokes darcy equations the method combines a time filter and backward euler scheme is second order accurate and provides at no extra complexity an estimate of the temporal error this approach post processes the solutions of backward euler scheme by adding three lines to original codes to increase the time accuracy from first order to second order we prove long time stability and error estimates of backward euler plus time filter with constant time stepsize moreover we extend the approach to variable time stepsize and construct adaptive algorithms numerical tests show convergence of our method and support the theoretical analysis

analysis of long time stability and errors of two partitioned methods for uncoupling evolutionary groundwater surface water flows the most effective simulations of the multiphysics coupling of groundwater to surface water must involve employing the best groundwater codes and the best surface water codes partitioned methods which solve the coupled problem by successively solving the subphysics problems have recently been studied for the stokes darcy coupling with convergence established over bounded time intervals with constants growing exponentially in t this report analyzes and tests two such partitioned noniterative domain decomposition methods for the fully evolutionary stokes darcy problem under a modest time step restriction of the form delta t leq c where c c physical parameters we prove unconditional long time over 0 leq t infty stability of both partitioned methods from this we derive an optimal error estimate that is uniform in time over 0 leq t infty

boundary integral solutions of coupled stokes and darcy flows an accurate computational method based on the boundary integral formulation is presented for solving boundary value problems for stokes and darcy flows the method also applies to problems where the equations are coupled across an interface through appropriate boundary conditions the adopted technique consists of first reformulating the singular integrals for the fluid quantities as single and double layer potentials then the layer potentials are regularized and discretized using standard quadratures as a final step the leading term in the regularization error is eliminated in order to gain one more order of accuracy the numerical examples demonstrate the increase of the convergence rate from first to second order and show a decrease in magnitude of the error the coupled problems require the computation of the gradient of the stokes velocity at the common interface this boundary condition is also written as a combination of single and double layer potentials so that the same approach can be used to compute it accurately extensive numerical examples show the increased accuracy gained by the correction terms

solving boundary value problems of ordinary differential equations with non separated boundary conditions abstract this paper focuses on solving the two point boundary value problem in which boundary conditions are systems of nonlinear equations the shooting method was used together with a combination of newton s method and broyden s method to update the initial values of the differential equations the experiments showed that the proposed method performed well in the sense that the overall amount of work was less than that of the newton shooting method

variational iteration method for elastodynamic green s functions abstract in this study a new application of the variational iteration method is presented we use this method to obtain approximations to 3d green s function for the dynamic system of anisotropic elasticity the numerical results obtained from convolution of green s function and data of the cauchy problem are compared with the exact solution for cubic media

decoupled schemes for a non stationary mixed stokes darcy model we study numerical methods for solving a non stationary mixed stokes darcy problem that models coupled fluid flow and porous media flow a decoupling approach based on interface approximation via temporal extrapolation is proposed for devising decoupled marching algorithms for the mixed model error estimates are derived and numerical experiments are conducted to demonstrate the computational effectiveness of the decoupling approach

efficient and long time accurate second order methods for the stokes darcy system we propose and study two second order in time implicit explicit methods for the coupled stokes darcy system that governs flows in karst aquifers and other subsurface flow systems the first method is a combination of a second order backward differentiation formula and the second order gear s extrapolation approach the second is a combination of the second order adams moulton and second order adams bashforth methods both algorithms only require the solution of decoupled stokes and darcy problems at each time step hence these schemes are very efficient and can be easily implemented using legacy codes we establish the unconditional and uniform in time stability for both schemes the uniform in time stability leads to uniform in time control of the error which is highly desirable for modeling physical processes e g contaminant sequestration and release that occur over very long time scales error estimates for fully discretized schemes using finite element spatial discretizations are derived nume

a two grid method of a mixed stokes darcy model for coupling fluid flow with porous media flow we study numerical methods for solving a coupled stokes darcy problem in porous media flow applications a two grid method is proposed for decoupling the mixed model by a coarse grid approximation to the interface coupling conditions error estimates are derived for the proposed method both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two grid approach for solving multimodeling problems potential extensions and future directions are discussed

codimension 1 subgroups and splittings of groups abstract we show that under certain circumstances a codimension 1 subgroup h of a finitely generated group g either provides a splitting of g as an amalgam or provides a codimension 1 subgroup of h in particular if g is hyperbolic and h is quasiconvex one gets a descending sequence of codimension 1 subgroups terminating at a splitting in the process we settle a conjecture of kropholler and roller for the case of quasiconvex subgroups of hyperbolic groups

a closed form approximation for the fractional black scholes model with transaction costs abstract in this paper we investigate option valuation problems under the fractional black scholes model the aim is to propose a pricing formula for the european option with transaction costs where the costs structure contains fixed costs a cost propositional to the volume traded and a cost proportional to the value traded precisely we provide an approximate solution of the nonlinear hoggard whalley wilmott equation the comparison results reveal that our approximate solutions are close to the numerical computations moreover the comparison results demonstrate that the price of the european option decreases as the hurst exponent increases

an efficient algorithm for solving troesch s problem abstract a new algorithm is presented for solving troesch s problem the numerical scheme based on the modified homotopy perturbation technique is deduced some numerical experiments are made compared with the variational iteration method and the adomian decomposition method the scheme is shown to be highly accurate and only a few terms are required to obtain accurate computable solutions finally the algorithm is applied to other problems

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 combination theorem for special cube complexes we prove that certain compact cube complexes have special nite covers this means they have nite covers whose fundamental groups are quasiconvex subgroups of right angled artin groups as a result we obtain linearity and the separability of quasiconvex subgroups for the groups we consider our result applies in particular to a compact negatively curved cube complex whose hyperplanes do not self intersect for a cube complex with word hyperbolic fundamental group we show that it is virtually special if and only if its hyperplane stabilizers are separable in a nal application we show that the fundamental groups of every simple type uniform arithmetic hyperbolic manifolds are cubical and virtually special

long time stability of four methods for splitting the evolutionary stokes darcy problem into stokes and darcy subproblems this report analyzes the long time stability of four methods for non iterative sub physics uncoupling for the evolutionary stokes darcy problem the four methods uncouple each timestep into separate stokes and darcy solves using ideas from splitting methods three methods uncouple sequentially while one is a parallel uncoupling method we prove long time stability of four splitting based partitioned methods under timestep restrictions depending on the problem parameters the methods include those that are stable uniformly in s 0 the storativity coefficient for moderate k m i n the minimum hydraulic conductivity uniformly in k m i n for moderate s 0 and with no coupling between the timestep and the spacial meshwidth

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

stochastic numerical treatment for solving troesch s problem abstract in this article the numerical techniques are presented for the solution of troesch s problem based on neural networks optimized with three different methods including particle swarm optimization pso active set as and pso hybridized with as pso as algorithms the variable transformation is applied in order to convert the original problem to a transformed problem which is relatively less stiff to solve feed forward artificial neural networks are used to model the transformed problem learning of adjustable parameters is made with pso as and pso as algorithms the proposed methodologies are applied to a number of cases for stiff and non stiff boundary value problems the comparative analyses are carried out with other standard numerical solutions as well as approximate analytical solver

a reliable algorithm for obtaining positive solutions for nonlinear boundary value problems abstract in this paper we propose an algorithm for solving the nonlinear two point boundary value problem that has at least one positive solution 1 6 for in a compatible interval our method stems mainly from combining the decomposition series solution obtained by adomian decomposition method with pade approximates the validity of the approach is verified through illustrative numerical examples