volterra fredholm integral equation of the first kind and spectral relationships here the solution in one two and three dimensional for the volterra fredholm integral equation of the first kind is obtained in the space l 2 w xc 0 t t using a numerical method the integral equation of volterra fredholm becomes a linear system of fredholm integral equation when that the kernel of fredholm integral takes a logarithmic form carleman function generalized potential function and macdonald function are considered as special cases

exponential p convergence analysis for stochastic bam neural networks with time varying and infinite distributed delays we discuss exponential p convergence for stochastic bam neural networks the delays here are multiple time varying and infinite distributed delays we establish a new l operator delay differential integral inequality delay dependent criteria ensuring exponential p convergence are obtained giving the detail estimations of the exponential p convergence ball this paper is concerned with the problem of global exponential p convergence for stochastic bam neural networks with time varying and infinite distributed delays by constructing a new delay differential integral inequality and a novel l operator differential integral inequality and coupling with stochastic analysis techniques some delay dependent sufficient conditions are derived to guarantee exponential p convergence and the state variables of the discussed stochastic bam neural networks are globally exponentially convergent to a ball in the state space with a pre specified convergence rate meanwhile the exponential p convergent balls are also estimated here the existence and the uniqueness of the equilibrium point needs not to be considered finally two examples with numerical simulations are given to illustrate the effectiveness of the theoretical results

goursat functions for an infinite plate with a generalized curvilinear hole in ζ plane we used a rational mapping function with complex constants to derive exact and close expressions of goursat functions for the first and second fundamental problems plane elasticity problems of an infinite plate weakened by a hole having arbitrary shape notable the area outside the hole is conformally mapped outside a unit circle by means of the rational mapping the complex variable method has been applied in the procedure and it transforms the fundamental problems to the integro differential equations that can be solved by using cauchy type integrals the hole takes different famous shapes which can be found throughout the nature like tunnels caves excavation in soil or rock etc many previous works have been considered as special cases of this work also many new cases can be derived from the problem

computational study of incompressible turbulent flows with method of characteristics the current study presents numerical investigation of incompressible turbulent flow momentum and continuity equations are coupled by the artificial compressibility method acm the one equation spalart allmaras turbulence model along with rans reynolds averaged navier stokes equations is used to calculate reynolds stresses in 2 d problems for convective fluxes a characteristic based cb finite volume solution has been developed also a revised jameson averaging avr method was implemented in comparison the proposed cb upwind scheme demonstrated very accurate results high stability and faster convergence for time discretization the fifth order runge kutta scheme is used as the convergence acceleration techniques the local time stepping and implicit residual smoothing were applied considering flow behavior suitable boundary conditions have been implemented cross flow around a horizontal circular cylinder at high reynolds numbers has been studied as a benchmark the results obtained using the new proposed scheme are in good agreement with the standard available solutions in the literature

fredholm integral equation with potential kernel and its structure resolvent the purpose of this paper is to establish and solve the fredholm integral equation of the second kind with potential kernel from the semi symmetric hertz problem for two different elastic materials in three dimensions the kernel of the problem is represented in the non homogeneous wave equation also the structure resolvent of the problem is obtained

periodic duffing delay equations with state dependent impulses conditions are obtained for the duffing equation with delay and state dependent impulses to admit a periodic solution

fredholm volterra integral equation with singular kernel in this paper under certain conditions a series in the legendre polynomials form is used to obtain the solution of fredholm volterra integral equation of the second kind in l 2 1 1 xc 0 t t the uniqueness of the solution is considered the kernel of fredholm integral term is established in a logarithmic form in position while the kernel of volterra integral term is a positive continuous function in time and belongs to the class c 0 t t the solution by series leads us to obtain an infinite system of linear algebraic equations where the convergence of this system is studied in the end of this paper the fredholm volterra integral equation of the first kind is established and its solution is discussed

the perturbed galerkin method for cauchy singular integral equations with constant coefficients we have considered the numerical solution of cauchy singular integral equations with constant coefficients via a polynomial based galerkin method l 2 and uniform convergence results are proved under holder continuity conditions on the kernel and right hand side and taking into account the quadrature errors produced when inner products are replaced by numerical quadratures these results generalize those of miel who considered only the case of equations of the first kind with index 0

numerical solution of volterra fredholm integral equations using the collocation method based on a special form of the muntz legendre polynomials abstract this paper presents a computational technique based on a special family of the muntz legendre polynomials to solve a class of volterra fredholm integral equations the relationship between the jacobi polynomials and muntz legendre polynomials in a particular state are expressed the proposed method reduces the integral equation into algebraic equations via the chebyshev gauss lobatto points so that the system matrix coefficients are obtained by the least squares approximation method the useful properties of the jacobi polynomials are exploited to analyze the approximation error the performance and accuracy of our method are examined with some illustrative examples

toeplitz matrix method and nonlinear integral equation of hammerstein type the existence and uniqueness solution of the nonlinear integral equation of hammerstein type with discontinuous kernel are discussed the normality and continuity of the integral operator are proved toeplitz matrix method is used as a numerical method to obtain a nonlinear system of algebraic equations also many important theorems related to the existence and uniqueness of the produced algebraic system are derived finally numerical examples when the kernel takes a logarithmic and carleman forms are discussed and the estimate error in each case is calculated

on the solution of a mixed nonlinear integral equation in this paper we consider a mixed nonlinear integral equation of the second kind in position and time the existence of a unique solution of this equation is discussed and proved a numerical method is used to obtain a system of harmmerstein integral equations of the second kind in position then the modified toeplitz matrix method as a numerical method is used to obtain a nonlinear algebraic system many important theorems related to the existence and uniqueness solution to the produced nonlinear algebraic system are derived the rate of convergence of the total error is discussed finally numerical examples when the kernel of position takes a logarithmic and carleman forms are presented and the error estimate in each case is calculated

four properties for complex potentials in power series form based on the basic equations of plane and anti plane problems and the feature of stress fields four important properties for complex potentials expressed in power series expansion in the plane and anti plane elastic fields are obtained first the complex potentials in the plane or anti plane elastic fields are both even functions when the stress states are symmetrical with regard to the origin next it is found that the coefficients of complex potentials in the plane elastic field must be real quantity when the stress states are symmetrical with regard to the x axis the last conclusion is that the complex potentials in the anti plane elastic field only have imaginary coefficients when the stress states are anti symmetric with regard to the x axis then based on the above conclusions some classic solutions are rearrived at which indicates the results derived in the paper are right and may simplify the process of constructing and solving the complex potential functions the present conclusions provide an efficient tool to discover the complex potentials in the sophisticated state

integral equation with macdonald kernel and its application to a system of contact problem a generalized potential theory method is used to construct a closed form solution of the axi symmetric contact problem for a finite system of impressing stamps of angular form in a plane into a half space occupying the domain

reproducing kernel method for solving fredholm integro differential equations with weakly singularity singular integral equations sies are often encountered in certain contact and fracture problems in solid mechanics numerical methods for solving sies have been the focus of much research including reproducing kernel methods however there are no reports on reproducing kernel methods for solving differential integral equations with weakly singular kernels we developed a reproducing kernel method for solving fredholm integro differential equations with weakly singular kernels in reproducing kernel hilbert space this involves changing a weakly singular kernel to a logarithm kernel to a kalman kernel weak singularity is removed by applying a smooth transformation to the kalman kernel solution representations are obtained in reproducing kernel hilbert space numerical experiments show that our reproducing kernel method is efficient

taylor collocation method and convergence analysis for the volterra fredholm integral equations in this paper the taylor collocation method is presented for numerically solving the volterra fredholm integral equations in terms of taylor polynomials this method transforms the integral equation to a matrix equation via the collocation points the convergence analysis of the collocation solution on the integral equation is given the method is computationally attractive and applications are demonstrated through illustrative examples

on the solution of linear and nonlinear integral equation the purpose of this paper is to establish the solution of fredholm volterra integral equation of the second kind in the space l 2 w xc 0 t considering the following when fredholm integral term in li 2 w and volterra integral term in 0 t are linear also each of fredholm or volterra integral term is linear while the other term is nonlinear here w is defined as the domain of integration with respect to position while t is consider as the time email protected 0 t t also the fredholm volterra integral equation of the first kind is established as special case of these work many special in one two and three dimensional problems of integral equation are considered representing the kernel of fredholm integral term in the form of logarithmic function carleman function potential and generalized potential function and macdonald function are considered

a solution of a nonlinear integral equation in this work we will prove the existence of integrable solution of nonlinear integral equation of type hammerstein volterra of the second kind by using the technique of measure of weak noncompactness and schauder fixed point theorem also the solution of the integral equation is obtained and studied

artificial compressibility characteristics based schemes for variable density incompressible multi species flows part i derivation of different formulations and constant density limit the paper presents various formulations of characteristics based schemes in the framework of the artificial compressibility method for variable density incompressible flows in contrast to constant density incompressible flows where the characteristics based variables reconstruction leads to a single formulation in the case of variable density flows three different schemes can be obtained henceforth labeled as transport conservative and hybrid schemes the conservative scheme results in pseudo compressibility terms in the multi species density reconstruction it is shown that in the limit of constant density the transport scheme becomes the original characteristics based scheme for incompressible flows but the conservative and hybrid schemes lead to a new characteristics based variant for constant density flows the characteristics based schemes are combined with second and third order interpolation for increasing the computational accuracy locally at the cell faces of the control volume numerical experiments for constant density flows reveal that all the characteristics based schemes result in the same flow solution but they exhibit different convergence behavior the multigrid implementation and numerical studies for variable density flows are presented in part ii of this study

invariant formulation for the minimum induced drag conditions of nonplanar wing systems under the hypotheses of linear potential flow and rigid wake aligned with the freestream a configuration invariant analytical formulation for the induced drag minimization of single wing nonplanar systems is presented following a variational approach the resulting euler lagrange integral equation in the unknown circulation distribution is obtained the kernel presents a singularity of the first order and an efficient computational method ideal for the early conceptual phases of the design is proposed munk s theorem on the normalwash and its relation with the geometry of the wing under optimal conditions is naturally obtained with the present method moreover munk s constant of proportionality not provided in his original work is demonstrated to be the ratio between the freestream velocity and the optimal aerodynamic efficiency the augmented munk s minimum induced drag theorem is then formulated additional induced drag theorems are demonstrated following the derivations of this invariant proced

non conservative and conservative formulations of characteristics based numerical reconstructions for incompressible flows summary an investigation of characteristics based cb schemes for solving the incompressible navierstokes equations in conjunction with the artiflcial compressibility approach is presented both nonconservative and conservative characteristics based numerical reconstructions are derived and their accuracy and convergence properties are assessed analytically and numerically we demonstrate by means of eigenvalue analysis that there are difierences in the spectral characteristics of these formulations that result in difierent convergence properties numerical tests for two and threedimensional ows reveal that the two formulations provide similar accuracy but the non conservative formulation converges faster copyright c 2000 john wiley sons ltd

iterative method and convergence analysis for a kind of mixed nonlinear volterra fredholm integral equation in this paper the iterative method is presented for numerically solving the nonlinear volterra fredholm integral equation first considering some conditions on k i and l i i 1 2 of the integral equation then we define the equidistance collocation points and the integral part of equation is discretized by newton cotes integration formula finally the approximate solutions of integral equation are obtain by iterative method the convergence analysis of the integral equation is given some numerical examples are given to illustrate the accuracy and dependability of the method

first passage times of two dimensional correlated processes given a two dimensional correlated diffusion process we determine the joint density of the first passage times of the process to some constant boundaries this quantity depends on the joint density of the first passage time of the first crossing component and of the position of the second crossing component before its crossing time first we show that these densities are solutions of a system of volterra fredholm first kind integral equations then we propose a numerical algorithm to solve it and we describe how to use the algorithm to approximate the joint density of the first passage times the convergence of the method is theoretically proved for bivariate diffusion processes we derive explicit expressions for these and other quantities of interest in the case of a bivariate wiener process correcting previous misprints appearing in the literature finally we illustrate the application of the method through a set of examples

integral equation of mixed type and integrals of orthogonal polynomials a method is used to obtain the general solution of the fredholm volterra integral equation of the first kind fviefk in the space l2 0 a c 0 t 0 x a 0 t t the kernel of the fredholm integal term is considered in a generalized discontinuous form which belongs to c 0 a 0 a while the kernel of volterra integral term is a positive continuous function in the class c 0 t many interesting cases of integrals of orthogonal polynomials and spectral relationships are obtained and established from this work

a high order characteristics upwind fv method for incompressible flow and heat transfer simulation on unstructured grids abstract this paper presents a new unstructured grid upwind finite volume algorithm for accurate numerical simulation of incompressible flows and convection heat transfer on unstructured grids it is an upwind method at both the differential equation level and discretized equation level based on the method of characteristics this is made possible with the introduction of chorin s j comput phys 2 1967 12 26 artificial compressibility formulation to the incompressible flow equations flow variables are calculated along characteristics and their initial values are interpolated based on the signs of the corresponding characteristic speed in addition an upwind biased interpolation method of third order accuracy is used for interpolating flow variables on unstructured grids with these inherent upwinding techniques for evaluating convection fluxes at control volume surfaces no artificial viscosity is required and the method is accurate and less sensitive to the grid orientation thus suitable for unstructured grid application the use of the finite volume method combined with unstructured grids makes the scheme very flexible in dealing with very complex boundary geometries while remaining to be fully conservative at the cell as well as global level the discretized equations are solved by an explicit multistage runge kutta time stepping scheme which is found to be efficient in terms of cpu and memory overheads a computer code has been developed which uses the numerical methods presented and a highly efficient edge based data structure for flux calculation and data storage a number of well documented test cases including 2d laminar flow in a channel with a backward facing step forced and natural convection flows have been calculated in order to validate the code and evaluate the performance of the numerical algorithm good agreement between the computed and measured results have been obtained for all the cases to demonstrate the accuracy of the third order scheme flow in another channel with a backward facing step studied by gartling int j numer meth fluids 1990 11 is simulated with both the third order and first order schemes it is shown that the third order scheme can produce a velocity profile across the channel that has perfect agreement with that of gartling local citation whilst the first order scheme cannot even predict the separation near the upper wall the proposed numerical methods are also used to calculate 3d incompressible inviscid flows and results show that the method is accurate and robust for general 3d simulation the 3d navier stokes code is later used to study a lid driven cavity flow at a reynolds number of 400 the unstructured grid used has 97 336 nodes and 455 625 tetrahedral elements with strong grid clustering near the walls the convergence rate is found to be satisfactory which shows that the method is also robust for 3d navier stokes simulation the results obtained agree well with those reported by jiang et al comput meth appl mech eng 114 109 1994 results obtained using the second order central scheme with artificial viscosity are also presented for comparison it is observed that the third order characteristics scheme is more accurate than the latter thus confirming its third order accuracy

periodic boundary value problem for the second order impulsive functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problem for second order functional differential equations by using the method of lower and upper solutions coupled with monotone iterative technique

global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics in this paper we shall consider the following nonlinear impulsive delay differential equation x t v t x t xn t m n xn t m t a e t 0 t tk x tk 1 1 bk x tk k 1 2 where m and n are positive integers v t and t are positive periodic continuous functions with period 0 in the nondelay case m 0 we show that the above equation has a unique positive periodic solution x t which is globally asymptotically stable in the delay case we present sufficient conditions for the global attractivity of x t our results imply that under the appropriate periodic impulsive perturbations the impulsive delay equation shown above preserves the original periodic property of the nonimpulsive delay equation in particular our work extends and improves some known results

periodic boundary value problem for the second order impulsive functional differential equations this paper considers the existence of extreme solutions of the periodic boundary value problems for the second order functional differential equations the novelty is that we introduce a new concept for lower and upper solutions and present that the method of lower and upper solutions coupled with monotone iterative technique is still valid meanwhile we extend previous results

integral equation and contact problem for a system of impressing stamps a method is used to construct a closed form solution of the axi symmetric contact problem for a finite system of impressing stamps of angular form in a plane into a half space the problem reduces to a complex mixed problem of the theory of elasticity in cylindrical coordinates

optimal approximation to a class of nonlinear evolution equations abstract in this paper we have developed and discussed a generalized difference method gdm for the approximation of a class of nonlinear evolution equations with integral items in one space dimension the main idea of the paper is to introduce a generalized volterra projection operator and we design a generalized difference formulation with a new approximate value of initial function which is of special importance for the error analysis then some theories of the generalized volterra projection operator are analyzed finally we deduce the optimal error estimates moreover some conclusions are obtained and our further research work is proposed

periodic boundary value problems for delay differential equations with impulses existence and approximation of solutions for an impulsive delay differential equation with periodic boundary value conditions are presented we use comparison principles and monotone iterative techniques

convergence analysis of hybrid functions method for two dimensional nonlinear volterra fredholm integral equations abstract an interesting and computationally efficient scheme is proposed for solving a class of two dimensional nonlinear volterra fredholm integral equations the collocation method in conjunction with two dimensional hybrid functions is utilized to convert these types of equations to a nonlinear system of equations that can be solved numerically by the newton s method the major advantages of this method are simplicity of performing and favorable convergence rate for an approximate solution the convergence analysis of the hybrid functions and the error bound of the presented method are discussed in detail moreover some numerical experiments are provided to confirm our theoretical analysis

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

on the weighted galerkin method of numerical solution of cauchy type singular integral equations the well known weighted galerkin method for the direct numerical solution of cauchy type singular integral equations of the first and the second kind based on the approximation of the unknown function by a finite series of appropriate orthogonal polynomials is shown to be identical to the corresponding method based on the reduction of the cauchy type singular integral equation to an equivalent fredholm integral equation of the second kind and the application to the latter of the weighted galerkin method this result permits the direct transfer of the whole set of convergence and rate of convergence results for the weighted galerkin method of numerical solution of fredholm integral equations with regular kernels to the case of cauchy type singular integral equations an application to the case where chebyshev polynomials are used is also made and the available convergence results for the direct weighted galerkin method are rederived with essentially no analysis

the galerkin method for singular integral equations revisited abstract in an earlier work the author has obtained error bounds for the galerkin method for solving cauchy singular integral equations discovering that the usually neglected constants contain the riemann zeta function when evaluated in the supremum norm the aim of this investigation is twofold to show that the occurrence of the riemann zeta function in the error bound for the chebyshev norm is sharp and secondly to use this result to obtain a class of forcing functions for which the method does not yield an approximate solution differing from the analytical one by at most a prescribed error tolerance these counterexamples indicate that in practical situations for functions exhibiting a behavior similar to the one presented here galerkin s method might not lead to an acceptable solution

on the numerical solutions of fredholm volterra integral equation toeplitz matrix method and the product nystrom method are described for mixed fredholm volterra singular integral equation of the second kind the results are compared with the exact solution of the integral equation the error of each method is calculated

fredholm volterra integral equation in contact problem in this work the solution of the integral equation of the mixed type in the domain w x y z email protected

integral equations and potential theortic type integrals of orthogonal polynomials abel s theorem is used to solve the fredholm integral equations of the first kind with gauss s hypergeometric kernel the case that the kernel takes general form is discussed in detail and the solution is given here the works of some authors are considered as special cases the discussion focuses on the three dimensional contact problems in the theory of elasticity with general kernel

periodic boundary value problem for non lipschitzian impulsive functional differential equations we consider a class of first order impulsive functional differential equations where the functional dependence is not necessarily a lipschitzian function the new maximum principle improves and extends previous results and uniqueness of solution between a lower and an upper solution for a particular nonlinear problem is presented we give conditions for existence of extremal solutions in an interval delimited by a lower and an upper solution

on the numerical treatment of the singular integral equation of the second kind here a numerical treatment for solving the integral equation of the second kind with cauchy kernel is presented the singular term has been removed and the solution in the legendre polynomial form has been used to obtain a system of linear algebraic equation this system is solved numerically

fredholm volterra integral equation of the first kind and contact problem regular and singular asymptotic methods are applied to one and two dimensional fredholm volterra integral equation f vie of the first kind that arise in the treatment of various two dimensional axisymmetric and three dimensional problems with mixed boundary conditions in the mechanics of continuous media the solution of the integral equation is obtained in the space l 2 w xc 0 t 0

numerical solution of integral equations 1 a survey of boundary integral equation methods for the numerical solution of laplace s equation in three dimensions 2 superconvergence 3 perturbed projection methods for various classes of operator and integral equations 4 numerical solution of parallel processors of two point boundary value problems of astrodynamics 5 introduction to the numerical solution of cauchy singular integral equations 6 convergence theorems for singular integral equations 7 planing surfaces 8 abel integral equations

on dynamic problem and integral equation in this work the fredholm integral equation of the second kind with logarithmic kernel is established from dynamic elastic problem such problem appears for example when a stamp of length 2a is impressed into the boundary of a strip y h by a variable force p t with time t 0 t t also the strip without fraction lies on a rigid elastic layer of thickness h the solution of the integral equation is obtained using chebyshev polynomial a numerical result is obtained for the problem

numerical solution for system of cauchy type singular integral equations with its error analysis in complex plane abstract in this paper the problem of finding numerical solution for a system of cauchy type singular integral equations of first kind with index zero is considered the analytic solution of such system is known but it is of limited use as it is a nontrivial task to use it practically due to the presence of singularity in the known solution itself therefore a residual based galerkin method is proposed with legendre polynomials as basis functions to find its numerical solution the proposed method converts the system of cauchy type singular integral equations into a system of linear algebraic equations which can be solved easily further hadamard conditions of well posedness are established for system of cauchy singular integral equations as well as for system of linear algebraic equations which is obtained as a result of approximation of system of singular integral equations with cauchy kernel the theoretical error bound is derived which can be used to obtain any desired accuracy in the approximate solution of system of cauchy singular integral equations the derived theoretical error bound is also validated with the help of numerical examples

numerical solution of nonlinear volterra fredholm hammerstein integral equations via collocation method based on radial basis functions abstract a numerical technique based on the spectral method is presented for the solution of nonlinear volterra fredholm hammerstein integral equations this method is a combination of collocation method and radial basis functions rbfs with the differentiation process drbf using zeros of the shifted legendre polynomial as the collocation points different applications of rbfs are used for this purpose the integral involved in the formulation of the problems are approximated based on legendre gauss lobatto integration rule the results of numerical experiments are compared with the analytical solution in illustrative examples to confirm the accuracy and efficiency of the presented scheme

periodic solutions for ordinary differential equations with sublinear impulsive effects abstract the continuation method of topological degree is used to investigate the existence of periodic solutions for ordinary differential equations with sublinear impulsive effects the applications of the abstract approach include the generalizations of some classical nonresonance theorem for impulsive equations for instance the existence theorem for asymptotically positively homogeneous differential systems and the existence theorem for second order equations with landesman lazer conditions

stability of artificial neural networks with impulses sufficient conditions are obtained for the existence and asymptotic stability of a unique equilibrium of a hopfield type neural network with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time both the continuous time and their corresponding discrete time networks are considered the sufficient conditions of the discrete time network do not restrict the step size appearing in the discretization process and these conditions approach as the step size tends to zero those of the conditions of the continuous time networks the sufficient conditions are in terms of the parameters of the network only and are easy to verify also when the impulsive jumps are absent the results reduce to those of the non impulsive systems

numerical methods of singular integral equation for solving some problem in fluid dynamic consider a contact problem of two different layers under certain conditions the aim of this work is obtaining the stress potential function between the two layers and obtaining the solution numerically using two different method toeplitz matrix method and product nystrom method numerical results are considered and the error in each case is computed

numerical solution of volterra fredholm integral equations based on e svr method in this paper we try to study the numerical methods for solving integral equations from a new perspective machine learning method by means of the idea of kernel e support vector regression machine e svr we construct an optimization modeling for a class of volterra fredholm integral equations and propose a novel numerical method for solving them the proposed method has a certain versatility and can be used to solve some other kinds of integral equations in order to verify the effectiveness of the proposed method we perform a series of comparative experiments with six specific volterra fredholm integral equations and a method proposed in wang et al 2014 experimental results show that the proposed method has a good approximation property

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

fredholm integral equation of the second kind with potential kernel a method is used to solve the fredholm integral equation of the second kind which is investigated from the semi symmetric hertz problem for two different elastic materials in three dimensions also the kernel is represented in the nonhomogeneous wave equation form

further convergence results for the weighted galerkin method of numerical solution of cauchy type singular integral equations the convergence of the weighted lalerkin method based on chcbvshen or jacobi polvnoinials for the direct numerical solution of one dimensional real cauchv tvpe singular integral equations of the first and of the second kind on a finite interval is proved under sufficientlv weak continuitv assumptions for the kernels and the right side functions of thc integral equations

on a symptotic methods for fredholm volterra integral equation of the second kind in contact problems a method is used to obtain the general solution of fredholm volterra integral equation of the second kind in the space l2 c 0 t 0 t t is the domain of integrations the kernel of the fredholm integral term belong to c and has a singular term and a smooth term the kernel of volterra integral term is a positive continuous in the class c 0 t while is the domain of integration with respect to the fredholm integral term besides the separation method the method of orthogonal polynomials has been used to obtain the solution of the fredholm integral equation the principal singular part of the kernel which corresponds to the selected domain of parameter variation is isolated the unknown and known functions are expanded in a chebyshev polynomial and an infinite algebraic system is obtained

galerkin s method for operator equations with nonnegative index with application to cauchy singular integral equations abstract we consider solving operator equation 1 hu ku f where h and k are bounded linear operators between two real hilbert spaces h1 and h2 operator h is assumed to have a finite dimensional nullspace n h and a bounded right inverse h1 h2 h1 and k is compact it follows that dim n h k dim n h so that to obtain uniqueness the m additional conditions 2 u k 1 bk k 1 2 h dim n h m are imposed where the k k 1m are an orthonormal basis for n h to solve 1 and 2 these equations are converted to an equivalent equation of the second kind to which galerkin s method is applied using the basis 1 2 m m 1 n it was shown that this method is equivalent to the method of weighted residuals when h 1 h the adjoint of h the results are applied to obtain convergence proofs of some numerical methods for solving several classes of cauchy singular integral equations whose kernels are only square integrable

lagrange collocation method for solving volterra fredholm integral equations in this paper the lagrange collocation method is used to solve the volterra fredholm integral equations this method transforms the system of the linear integral equations into matrix equations via lagrange collocation points the lagrange collocation solution of the three kinds of volterra fredholm integral equations and the error estimate of these equations are given some numerical examples are presented to illustrate the accuracy of the method

galerkin solution of a singular integral equation with constant coefficients galerkin methods are used to approximate the singular integral equation email protected x email protected 1 email protected t email protected 1 1k t x f t dt f x 10 are constants in this case f is decomposed as f x 1 x a 1 x bu x where email protected 0 0 is a small enough constant

a multidimensional characteristic based method for making incompressible flow calculations on unstructured grids this paper presents a new multidimensional characteristic based scheme mcb for numerical simulation of incompressible flows on unstructured grids in conjunction with the artificial compressibility method the original mcb scheme has been proposed by the authors already and this research is the extension of the aforementioned scheme to unstructured grids the significant difference between mcb and the conventional characteristic based scheme cb is the multidimensional nature of the scheme which allows information to propagate in any direction instead of only normal to the cell interface in addition local time stepping and the residual smoothing technique have been used for convergence acceleration the accuracy and utility of the proposed scheme have been studied by means of numerical tests for different reynolds numbers and the results obtained using the new scheme are in good agreement with the standard benchmark solution in the literature

numerical solution of volterra fredholm integral equations using legendre collocation method a numerical method for solving the volterra fredholm integral equations is presented the method is based upon shifted legendre polynomials approximation the properties of shifted legendre polynomials are first presented these properties together with the shifted gauss legendre nodes are then utilized to reduce the volterra fredholm integral equations to the solution of a matrix equation an estimation of the error is given illustrative examples are included to demonstrate the validity and applicability of the technique

numerical solution of fredholm volterra integral equation in one dimension with time dependent in this paper we consider fredholm volterra integral equation in one dimension with time dependent the kernel of the fredholm term is assumed to be singular while the kernel of volterra term is continuous the existence of the solution is proved and a numerical method is presented to get an approximate to such solution

short note on the characteristics based acm for incompressible flows in this paper the revised characteristics based cb method for incompressible flows recently derived by neofytou p neofytou revision of the characteristic based scheme for incompressible flows j comput phys 222 2007 475 484 has been further investigated we have derived all the formulas for pressure and velocities from this revised cb method which is based on the artificial compressibility method acm a j chorin a numerical solution for solving incompressible viscous flow problems j comput phys 2 1967 12 then we analyze the formulations of the original cb method d drikakis p a govatsos d e papatonis a characteristic based method for incompressible flows int j numer meth fluids 19 1994 667 685 e shapiro d drikakis non conservative and conservative formulations of characteristics numerical reconstructions for incompressible flows int j numer meth eng 66 2006 1466 1482 d drikakis p k smolarkiewicz on spurious vortical structures j comput phys 172 2001 309 325 f mallinger d drikakis instability in three dimensional unsteady stenotic flows int j heat fluid flow 23 2002 657 663 e shapiro d drikakis artificial compressibility characteristics based schemes for variable density incompressible multi species flows parts i derivation of different formulations and constant density limit j comput phys 210 2005 584 607 y zhao b zhang a high order characteristics upwind fv method for incompressible flow and heat transfer simulation on unstructured grids comput meth appl mech eng 190 5 7 2000 733 756 to investigate their consistency with the governing flow equations after convergence has been achieved furthermore we have implemented both formulations in an unstructured grid finite volume solver y zhao b zhang a high order characteristics upwind fv method for incompressible flow and heat transfer simulation on unstructured grids comput meth appl mech eng 190 5 7 2000 733 756 detailed numerical experiments show that both methods give almost identical solutions and convergence rates both can generate solutions which agree well with published results and experimental measurements we thus conclude that both methods being upwind schemes designed for the acm have the same performances in terms of accuracy and convergence speed even though the revised method is more complex with less stringent assumptions made while the original cb method is simpler due to the use of extra simplifying assumptions

numerical solution of nonlinear mixed volterra fredholm integral equations in complex plane via pqws abstract this paper presents an efficient numerical method for solving nonlinear mixed volterra integral equations in the complex plane the method is based on the fixed point iteration procedure in each iteration of this method periodic quasi wavelets are used as basis functions to approximate the solution also using the banach fixed point theorem some results concerning the error analysis are obtained finally some numerical examples show the implementation and accuracy of this method

exponential stability and periodic oscillatory solution in bam networks with delays both exponential stability and periodic oscillatory solution of bidirectional associative memory bam networks with axonal signal transmission delays are considered by constructing suitable lyapunov functional and some analysis techniques some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of bam with delays these conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for bam with delays in addition two examples are given to illustrate the results

stability of bidirectional associative memory networks with impulses abstract by using lyapunov functional and some analysis technique sufficient conditions are obtained for the existence and asymptotic stability of a unique equilibrium of a bidirectional associative memory bam neutral network with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time the sufficient conditions are in terms of the parameters of the network only and are easy to verify