using triangular orthogonal functions for solving fredholm integral equations of the second kind the present work proposes a method for solving fredholm integral equations this is demonstrated by using a complementary pair of orthogonal triangular functions set derived from the well known block pulse functions set the operational matrices for integration product of two triangular functions and some formulas for calculating definite integral of them are derived and utilized to reduce the solution of fredholm integral equation to the solution of algebraic equations illustrative examples are included to show the high accuracy of the estimation and to demonstrate validity and applicability of the method

legendre polynomial solutions of high order linear fredholm integro differential equations in this study a legendre collocation matrix method is presented to solve high order linear fredholm integro differential equations under the mixed conditions in terms of legendre polynomials the proposed method converts the equation and conditions to matrix equations by means of collocation points on the interval 1 1 which corresponding to systems of linear algebraic equations with legendre coefficients thus by solving the matrix equation legendre coefficients and polynomial approach are obtained also examples that illustrate the pertinent features of the method are presented and by using the error analysis the results are discussed

two dimensional shifted legendre polynomials operational matrix method for solving the two dimensional integral equations of fractional order abstract this work approximates the unknown functions based on the two dimensional shifted legendre polynomials operational matrix method 2d slpom for the numerical solution of two dimensional fractional integral equations the present method reduces these equations to a system of algebraic equations and then this system will be solved numerically by newton s method moreover an estimation of the error bound for this algorithm will be shown by preparing some theorems some examples are presented to demonstrate the validity and applicability of the proposed method with respect to the two dimensional block pulse functions method 2d bpfs and two dimensional bernstein polynomials operational matrix method 2d bpom

growth and poles of meromorphic solutions of some difference equations abstract this paper is devoted to studying the growth property and the pole distribution of meromorphic solutions f of some complex difference equations with all coefficients being rational functions or of growth s r f we find the lower bound of the lower order or the relation between lower order and the convergence exponent of poles of meromorphic solutions of such equations

on multiply connected fatou components in iteration of meromorphic functions abstract let f c c be a transcendental meromorphic function with at most finitely many poles we mainly investigated the existence of the baker wandering domains of f z and proved among others that if f z has a baker wandering domain u then for all sufficiently large n f n u contains a round annulus whose module tends to infinity as n and so for some 0 d 1 m c r a f d m c r a f r g where g is a set of positive numbers with infinite logarithmic measure therefore we give out several criterion conditions for non existence of the baker wandering domains

min max and min max regret versions of combinatorial optimization problems a survey abstract min max and min max regret criteria are commonly used to define robust solutions after motivating the use of these criteria we present general results then we survey complexity results for the min max and min max regret versions of some combinatorial optimization problems shortest path spanning tree assignment min cut min s t cut knapsack since most of these problems are np hard we also investigate the approximability of these problems furthermore we present algorithms to solve these problems to optimality

numerical solution of integro differential equations of high order by wavelet basis its algorithm and convergence analysis abstract this paper presents for the first time numerical solutions for this particular type of integro differential equations according to equations which will be introduced suitable wavelet galerkin method is provided using wavelet basis in the space c r l 2 r 0 that c r is the holder space of exponent this approach has two advantages first the wavelets basis are arbitrary it means that any differentiable wavelets basis can be used second the desired orders for this equation are the reasons for involving a wide variety of these types of equations the algorithm and convergence analysis of this scheme are described numerical examples plots and tablets of errors confirm the applicability and the validity of the proposed method

erratum to numerical solution of linear fredholm integral equation by using hybrid taylor and block pulse functions appl math comput 149 2004 799 806 abstract this is an erratum to the published paper numerical solution of linear fredholm integral equation by using hybrid taylor and block pulse functions by maleknejad and mahmoudi where there are some scientific errors after considering these errors we attempt to rectify them by presenting correct approach and formulae moreover by means of some numerical examples we illustrate the accuracy of solutions after applying the correct formulae

a new bound for the midpoint solution in minmax regret optimization with an application to the robust shortest path problem abstract minmax regret optimization aims at finding robust solutions that perform best in the worst case compared to the respective optimum objective value in each scenario even for simple uncertainty sets like boxes most polynomially solvable optimization problems have strongly np complete minmax regret counterparts thus heuristics with performance guarantees can potentially be of great value but only few such guarantees exist a popular heuristic for combinatorial optimization problems is to compute the midpoint solution of the original problem it is a well known result that the regret of the midpoint solution is at most 2 times the optimal regret besides some academic instances showing that this bound is tight most instances reveal a way better approximation ratio we introduce a new lower bound for the optimal value of the minmax regret problem using this lower bound we state an algorithm that gives an instance dependent performance guarantee for the midpoint solution that is at most 2 the computational complexity of the algorithm depends on the minmax regret problem under consideration we show that our sharpened guarantee can be computed in strongly polynomial time for several classes of combinatorial optimization problems to illustrate the quality of the proposed bound we use it within a branch and bound framework for the robust shortest path problem in an experimental study comparing this approach with a bound from the literature we find a considerable improvement in computation times

on the relationship between the lower order of coefficients and the growth of solutions of differential equations abstract some criteria for entire coefficients a z and b z are given in terms of the lower order forcing the solutions of f a z f b z f 0 to grow fast in the literature similar criteria have been published in terms of the usual order the case when the coefficient a z has an asymptotic growth t r a log m r a 0 1 outside of an exceptional set is also discussed previously laine wu 2000 and kim kwon 2001 have made use of this asymptotic growth in the case 1

the theoretical foundation of the adomian method abstract in this paper we work out the theoretical basis of the adomian method this powerful method that g adomian has developed in the beginning of the 1980 s supplies analytical approximations to the solution of many kinds of equations thanks to our decomposition theory we justify the practical method and we generalize the convergence results obtained by y cherruault afterward we explain how to solve rigorously equations with linear nonlinear or composed operator and also equations with several terms or with a second member

minmax regret combinatorial optimization problems with ellipsoidal uncertainty sets we consider robust counterparts of uncertain combinatorial optimization problems where the difference to the best possible solution over all scenarios is to be minimized such minmax regret problems are typically harder to solve than their nominal non robust counterparts while current literature almost exclusively focuses on simple uncertainty sets that are either finite or hyperboxes we consider problems with more flexible and realistic ellipsoidal uncertainty sets we present complexity results for the unconstrained combinatorial optimization problem the shortest path problem and the minimum spanning tree problem to solve such problems two types of cuts are introduced and compared in a computational experiment

approximation of min max and min max regret versions of some combinatorial optimization problems this paper investigates for the first time in the literature the approximation of min max regret versions of classical problems like shortest path minimum spanning tree and knapsack for a constant number of scenarios we establish fully polynomial time approximation schemes for the min max versions of these problems using relationships between multi objective and min max optimization using dynamic programming and classical trimming techniques we construct a fully polynomial time approximation scheme for min max regret shortest path we also establish a fully polynomial time approximation scheme for min max regret spanning tree and prove that min max regret knapsack is not at all approximable for a non constant number of scenarios in which case min max and min max regret versions of polynomial time solvable problems usually become strongly np hard non approximability results are provided for min max regret versions of shortest path and spanning tree

a numerical method for solving fredholm volterra integral equations in two dimensional spaces using block pulse functions and an operational matrix in this paper the block pulse functions bpfs and their operational matrix are used to solve two dimensional fredholm volterra integral equations f vie this method converts f vie to systems of linear equations whose solutions are the coefficients of block pulse expansions of the solutions of f vie finally some numerical examples are presented to show the efficiency and accuracy of the method

a comparative study of numerical integration based on haar wavelets and hybrid functions a quadrature rule based on uniform haar wavelets and hybrid functions is proposed to find approximate values of definite integrals the wavelet based algorithm can be easily extended to find numerical approximations for double triple and improper integrals the main advantage of this method is its efficiency and simple applicability error estimates of the proposed method alongside numerical examples are given to test the convergence and accuracy of the method

a modified homotopy perturbation method for solving the nonlinear mixed volterra fredholm integral equation the purpose of this paper is to obtain the approximation solution of the strongly nonlinear mixed volterra fredholm integral equation vfie for some strongly nonlinear problems the traditional homotopy perturbation method is divergent so we propose a modified homotopy perturbation method which is still convergent when solving the strongly nonlinear mixed vfie by means of this method an algorithm is successfully established for solving the strongly nonlinear mixed vfie and the convergence of the algorithm is proved strictly finally several examples are presented to illustrate the application of the algorithm

a new computational method for volterra fredholm integral equations abstract the main purpose of this article is to demonstrate the use of the adomian decomposition method for mixed nonlinear volterra fredholm integral equations a bound is also given for the adomian decomposition series finally numerical examples are presented to illustrate the implementation and accuracy of the decomposition method

asymptotic expansion for the trapezoidal nystro m method of linear volterra fredholm equations abstract integral equations of mixed volterra fredholm type arise in various physical and biological problems in the present paper we study the particular trapezoidal nystrom method and we obtain the asymptotic error expansion for the trapezoidal nystrom solution of the linear volterra fredholm equation so the richardson extrapolation can be applied this will increase the accuracy of the numerical solution greatly some numerical examples are given to illustrate this theory

growth of solutions of second order linear differential equations abstract this paper is devoted to studying the growth of solutions of equations of type f h z e a z f q z f h z where h z q z and h z are entire functions of order at most one we prove four theorems of such type improving previous results due to gundersen and chen

new ideas for proving convergence of decomposition methods in this paper we give new formulae which calculate easily the adomian s polynomials used in decomposition methods then the proof of convergence of the adomian s technique becomes almost obvious by using a weak hypothesis on the nonlinear operator of the functional equation

lower order and baker wandering domains of solutions to differential equations with coefficients of exponential growth abstract we investigate transcendental entire solutions of complex differential equations f a z f h z where the entire function a z has a growth property similar to the exponential functions and h z is an entire function of order less than that of a z we first prove that the lower order of the entire solution to the equation is infinity by using our result on the lower order we prove the entire solution does not bear any baker wandering domains

solving second kind integral equations with hybrid chebyshev and block pulse functions in this paper we use a combination of chebyshev and block pulse functions on the interval 0 1 to solve the linear integral equation of the second kind we convert the integral equation to a system of linear equations we show that our estimates have a good degree of accuracy

the numerical solution of the non linear integro differential equations based on the meshless method this article investigates the numerical solution of the nonlinear integro differential equations the numerical scheme developed in the current paper is based on the moving least square method the moving least square methodology is an effective technique for the approximation of an unknown function by using a set of disordered data it consists of a local weighted least square fitting valid on a small neighborhood of a point and only based on the information provided by its n closet points hence the method is a meshless method and does not need any background mesh or cell structures the error analysis of the proposed method is provided the validity and efficiency of the new method are demonstrated through several tests

fatou sets of entire solutions of linear differential equations abstract this paper is devoted to studying the dynamical properties of solutions of f a z f 0 where a z is an entire function of finite order with some added conditions on a z we prove that all the fatou components of e z are simply connected provided that e f 1 f 2 and f 1 f 2 are two linearly independent solutions of such equations

a hybrid legendre block pulse method for mixed volterra fredholm integral equations abstract mixed volterra fredholm integral equations can arise from mathematical modelling of the spatio temporal development of an epidemic in this paper a hybrid legendre block pulse method is used to provide solutions to a general integral equation of this type the main idea of this approach is to reduce a volterra fredholm integral equation to a system of algebraic equations an order convergence analysis is provided the accuracy of the proposed method is then confirmed by solving some problems the first being a nonlinear epidemic problem

on the complexity of minmax regret linear programming abstract we consider linear programming problems with uncertain objective function coefficients for each coefficient of the objective function an interval of uncertainty is known and it is assumed that any coefficient can take on any value from the corresponding interval of uncertainty regardless of the values taken by other coefficients it is required to find a minmax regret solution this problem received considerable attention in the recent literature but its computational complexity status remained unknown we prove that the problem is strongly np hard this gives the first known example of a minmax regret optimization problem that is np hard in the case of interval data representation of uncertainty but is polynomially solvable in the case of discrete scenario representation of uncertainty

a double oracle approach to minmax regret optimization problems with interval data in this paper we provide a generic anytime lower bounding procedure for minmax regret optimization problems we show that the lower bound obtained is always at least as accurate as the lower bound recently proposed by chassein and goerigk 3 this lower bound can be viewed as the optimal value of a linear programming relaxation of a mixed integer programming formulation of minmax regret optimization but the contribution of the paper is to compute this lower bound via a double oracle algorithm 10 that we specify the double oracle algorithm is designed by relying on a game theoretic view of robust optimization similar to the one developed by mastin et al 9 and it can be efficiently implemented for any minmax regret optimization problem whose standard version is easy we describe how to efficiently embed this lower bound in a branch and bound procedure finally we apply our approach to the robust shortest path problem our numerical results show a significant gain in the computation times compared to previous approaches in the literature

continuous time collocation methods for volterra fredholm integral equations integral equations of mixed volterra fredholm type arise in various physical and biological problems in the present paper we study continuous time collocation time discretization and their global and discrete convergence properties

a note on finding minimum cost edge disjoint spanning trees let g be an undirected graph with n vertices and m edges such that each edge has a real valued cost we consider the problem of finding a set of k edge disjoint spanning trees in g of minimum total edge cost this problem can be solved in polynomial time by the matroid greedy algorithm we present an implementation of this algorithm that runs in o m log m k2n2 time if all edge costs are the same the algorithm runs in o k2n2 time the algorithm can also be extended to find the largest k such that k edge disjoint spanning trees exist in o m2 time we mention several applications of the algorithm

an iterative solution for the second kind integral equations using radial basis functions the purpose of this paper is to present a new method based on radial basis functions rbfs and iterative procedure for the solution of linear integral equations of fredholm and volterra types of the second kind to obtain a primary approximate solution the collocation method with a small number of nodes based on the rbfs and their first order derivatives can be adapted moreover we present an iterative procedure from the integral equation to improve the accuracy of solution numerical examples show that our approach has the potentiality to become an efficient method

solving second kind integral equations by galerkin methods with hybrid legendre and block pulse functions in this paper we use a combination of legendre and block pulse functions on the interval 0 1 to solve the linear integral equation of the second kind we convert the integral equation to a system of linear equations we show that our estimates have a good degree of accuracy

a benders decomposition approach for the robust spanning tree problem with interval data abstract the robust spanning tree problem is a variation motivated by telecommunications applications of the classic minimum spanning tree problem in the robust spanning tree problem edge costs lie in an interval instead of having a fixed value interval numbers model uncertainty about the exact cost values a robust spanning tree is a spanning tree whose total cost minimizes the maximum deviation from the optimal spanning tree over all realizations of the edge costs this robustness concept is formalized in mathematical terms and is used to drive optimization this paper describes a new exact method based on benders decomposition for the robust spanning tree problem with interval data computational results highlight the efficiency of the new method which is shown to be very fast on all the benchmarks considered and in particular on those that were harder to solve for the methods previously known

asymptotic error expansion for the nystro m method for a nonlinear volterra fredholm integral equation in this paper we study the numerical solution of general nonlinear mixed volterra fredholm integral equations by the trapezoidal nystrom method it focuses on the derivation and analysis of asymptotic error expansion of the nystrom solution providing the basis for richardson s extrapolation this will greatly increase the accuracy of the numerical solution some numerical results are given to illustrate this theory

solution of physical problems by decomposition recent generalizations are discussed and results are presented for the theory and applications of the decomposition method application is made to the duffing equation with an error of 0 0001 in only four terms and less than 10 16 in thirteen terms of the decomposition series application is also made to a dissipative wave equation a matrix riccati equation and advection diffusion nonlinear transport

convergence of adomian s method applied to differential equations this paper deals with a new proof of convergence of adomian s method applied to differential equations we also give new formulae and properties and we suggest a simple computational form for adomian s polynomials

numerical solution of nonlinear fredholm integral equations of the second kind using haar wavelets in this work we present a computational method for solving nonlinear fredholm integral equations of the second kind which is based on the use of haar wavelets error analysis is worked out that shows efficiency of the method finally we also give some numerical examples

hybrid legendre block pulse functions for the numerical solutions of system of nonlinear fredholm hammerstein integral equations in this paper the numerical technique based on hybrid legendre block pulse function has been developed to approximate the solution of system of nonlinear fredholm hammerstein integral equations these functions are formed by the hybridization of legendre polynomials and block pulse functions these functions are orthonormal and have compact support on 0 1 the proposed method reduces the system of integral equations to a system of nonlinear algebraic equations that can be solved easily by any usual numerical method the numerical results obtained by the presented method have been compared with those obtained by legendre wavelet method lwm numerical examples are presented to illustrate the accuracy of the method

solving system of volterra fredholm integral equations with bernstein polynomials and hybrid bernstein block pulse functions this work approximates the unknown functions based on the bernstein polynomials and hybrid bernstein block pulse functions in conjunction with the collocation method for the numerical solution of system of fredholm volterra integral equations in both methods the system of integral equations is approximated by the gauss quadrature formula with respect to the legendre weight function the proposed methods reduce the system of integral equations to a system of algebraic equations that can be easily solved by any usual numerical methods moreover the convergence analysis of these algorithms will be shown by preparing some theorems numerical experiments are presented to show the superiority and efficiency of proposed methods in comparison with some other well known methods

a reliable treatment for mixed volterra fredholm integral equations the main goal of this paper is to demonstrate the use of the modified decomposition method for mixed nonlinear volterra fredholm integral equations the modified method combined with the noise terms phenomena may provide the exact solution by using two iterations only two numerical illustrations are given to show the pertinent features of the technique

numerical solution of integral equations system of the second kind by block pulse functions abstract this paper endeavors to formulate block pulse functions to propose solutions for the fredholm integral equations system to begin with we describe the characteristic of block pulse functions and will go on to indicate that through this method a system of fredholm integral equations can be reduced to an algebraic equation numerical examples presented to illustrate the accuracy of the method

numerical solution of non linear fredholm integral equations by using multiwavelets in the petrov galerkin method in this paper we use the wavelet petrov galerkin wpg method for solving one of the most important cases in non linear fredholm integral equations which is called hammerstein equations we suppose that the trial space and the test space that are used in this method to be piecewise polynomials space also we use alpert s multiwavelets as the bases for these spaces such that the wavelet basis for the test space constructed from lower degree polynomials than the trial space finally for showing efficiency of this method we use some numerical examples

on the numerical solution of nonlinear volterra fredholm integral equations by collocation methods particular cases of nonlinear mixed volterra fredholm integral equations of the second kind arise in the mathematical modeling of the spatio temporal development of an epidemic this paper is concerned with the numerical solution of general integral equations of this type by continuous time and discrete time spline collocation methods its focus is on the derivation and analysis of methods of high order of convergence

low cost numerical solution for three dimensional linear and nonlinear integral equations via three dimensional jacobi polynomials in recent years numerical methods have been introduced to solve two dimensional volterra and fredholm integral equations in this study a numerical scheme is constructed to solve classes of linear and nonlinear three dimensional integral equations volterra fredholm and mixed volterrafredholm this operational approach is proposed to easily and directly solve these equations at low computational costs the scheme is based on the jacobi polynomials on the interval 0 1 where three variable jacobi polynomials are introduced and their operational matrices of integration and product are derived compared to other existing methods for multidimensional problems the jacobi operational method eliminates the time consuming computations and solely employs the one dimensional operational matrix to construct corresponding multidimensional operational matrices the absolute error of the proposed method is almost constant on the studied interval even at higher dimensions confirming the stability of the proposed operational jacobi method required theorems on the convergence of the method are proved in jacobi weighted sobolev space it is established that the error function vanishes as n increases the method is evaluated using several illustrative examples which indicate the proposed method with lesser computational size compared to the blockpulse functions differential transform and degenerate kernel methods

robust optimization methodology and applications robust optimization ro is a modeling methodology combined with computational tools to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set the paper surveys the main results of ro as applied to uncertain linear conic quadratic and semidefinite programming for these cases computationally tractable robust counterparts of uncertain problems are explicitly obtained or good approximations of these counterparts are proposed making ro a useful tool for real world applications we discuss some of these applications specifically antenna design truss topology design and stability analysis synthesis in uncertain dynamic systems we also describe a case study of 90 lps from the netlib collection the study reveals that the feasibility properties of the usual solutions of real world lps can be severely affected by small perturbations of the data and that the ro methodology can be successfully used to overcome this phenomenon

numerical solution of the mixed volterra fredholm integro differential multi term equations of fractional order abstract this paper aims to introduce two effective numerical approaches for solving the mixed volterra fredholm integro differential equation of fractional order and multi order with initial values despite the fact that the second approach transfers the integro differential equations into a system of algebraic equations through the usage of operational matrices these problems can be transferred to a system of algebraic equations by expanding the solution s highest order derivative through the block pulse functions bpfs this is done by using the generalized operational matrices of bpfs for differentiation along with the fractional calculus properties in the first scheme in which convergence of the solution obtained has been shown in the following the accuracy and applicability of two proposed approaches will be compared by some relevant numerical examples for which the exact solution is known

comparison of legendre polynomial approximation and variational iteration method for the solutions of general linear fredholm integro differential equations in this study it is shown that the numerical solutions of linear fredholm integro differential equations obtained by using legendre polynomials can also be found by using the variational iteration method furthermore the numerical solutions of the given problems which are solved by the variational iteration method obviously converge rapidly to exact solutions better than the legendre polynomial technique additionally although the powerful effect of the applied processes in legendre polynomial approach arises in the situations where the initial approximation value is unknown it is shown by the examples that the variational iteration method produces more certain solutions where the first initial function approximation value is estimated in this paper the legendre polynomial approximation lpa and the variational iteration method vim are implemented to obtain the solutions of the linear fredholm integro differential equations and the numerical solutions with respect to these methods are compared

on a constant factor approximation for minmax regret problems using a symmetry point scenario abstract in order to find a robust solution under an unknown linear cost function it will be considered the minmax regret criterion it is assumed the vector of costs can take on values from a given uncertainty set the resulting optimization model has been extensively analyzed in the literature when the uncertain costs are modeled by closed intervals unfortunately except for rare applications this problem has np hard complexity which has led to the appearance of approximated methods seeking for good solutions in a short computational time the most recent approaches solve the deterministic version of the optimization problem under the midpoint scenario that realization in which each cost takes the midpoint of the closed interval proceeding in this way it can be obtained a 2 approximation for a wide class of minmax regret optimization models in this paper it is shown how this approach can be extended to a new class of minmax regret problems including more general uncertainty sets

new construction of wavelets base on floor function in this paper the properties of the floor function has been used to find a function which is one on the interval 0 1 and is zero elsewhere the suitable dilation and translation parameters lead us to get similar function corresponding to the interval a b these functions and their combinations enable us to represent the stepwise functions as a function of floor function we have applied this method on haar wavelet sine cosine wavelet block pulse functions and hybrid fourier block pulse functions to get the new representations of these functions

posteriori error estimates for the nonlinear volterra fredholm integral equations abstract we study the numerical approximation of the nonlinear volterra fredholm integral equations by combining the discrete time collocation method 1 and the new formulation of kumar and sloan 2 which converts an integral equation of the conventional hammerstein form into a conductive form for approximation by a collocation method the intrinsic merit of this alternative formulation lies in its computational savings posteriori error estimates of the method for two typical nonlinearities i e algebraic and exponential nonlinearity are obtained some remarks on the generalization of the method to higher dimensional cases are offered and finally some numerical examples are given