logarithmic corrections and finite size scaling in the two dimensional 4 state potts model we analyze the scaling and finite size scaling behavior of the two dimensional 4 state potts model we find new multiplicative logarithmic corrections for the susceptibility in addition to the already known ones for the specific heat we also find additive logarithmic corrections to scaling some of which are universal we have checked the theoretical predictions at criticality and off criticality by means of high precision monte carlo data

two dimensional percolation logarithmic corrections to the critical behaviour from series expansions analyses several extant series for the mean cluster size the zeroth moment of the pair connectedness and the percolation probability for bond and site percolation on two dimensional lattices with a view to detecting possible logarithmic corrections the logarithmic correction exponent z is found to be in the range 0 or z or 0 15 and our analysis also provides some new information about the critical exponents gamma and beta

a chebyshev approximation for solving nonlinear integral equations of hammerstein type abstract a numerical method for solving fredholm volterra hammerstein integral equations is presented this method is based on replacement of the unknown function by truncated series of well known chebyshev expansion of functions the quadrature formula which we use to calculate integral terms can be estimated by fast fourier transform fft the numerical examples and the number of operations show the advantages of this method to some other usual methods

new approach for numerical solution of hammerstein integral equations in this paper we use a numerical procedure for solving a class of nonlinear integral equations of the hammerstein type using the globally defined sinc basis functions properties of the sinc procedure are utilized to reduce the computation of the hammerstein equations to some algebraic equations we used some numerical examples to illustrate the accuracy and the implementation of the method

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

efficient chebyshev collocation methods for solving optimal control problems governed by volterra integral equations the main purpose of this work is to provide efficient chebyshev collocation methods for solving optimal control problems ocps governed by volterra integral equations the basic principle of our approach is to approximate the state and control using the chebyshev polynomials and collocate the dynamic constraints at the chebyshev type points furthermore we present an exact efficient and stable approach for computing the associated chebyshev integration matrices numerical results on benchmark ocps demonstrate the spectral rate of convergence for the proposed methods

an iterative multistep kernel based method for nonlinear volterra integral and integro differential equations of fractional order abstract an iterative multistep kernel based method is proposed for the nonlinear volterra integral equations and nonlinear volterra integro differential equations of fractional order which can produce reliable globally smooth numerical solutions an error estimate of the positive definite kernel interpolation and the convergence and error analysis of the proposed iterative scheme are investigated here we focused on positive definite radial basis kernels and further a new and applicable shape parameter selection strategy is proposed the proposed multi step method set up and solve several small local problems instead of a single large problem which makes it suitable for problems with long time simulations in order to show the efficiency and versatility of the proposed method some numerical experiments are reported the comparison of the numerical results with the analytical solutions and the best reported results in the literature confirm the good accuracy and applicability of the proposed method

existence of solutions to nonlinear hammerstein integral equations and applications abstract in this paper we study the existence and multiplicity of solutions of the operator equation k f u u in the real hilbert space l 2 g under certain conditions on the linear operator k we establish the conditions on f which are able to guarantee that the operator equation has at least one solution a unique solution and infinitely many solutions respectively the monotone operator principle and the critical point theory are employed to discuss this problem respectively in argument quadratic root operator k 1 2 and its properties play an important role as an application we investigate the existence and multiplicity of solutions to fourth order boundary value problems for ordinary differential equations with two parameters and give some new existence results of solutions

the q state potts ferromagnet on d dimensional hypercubic lattices we use a high temperature star graph expansion to compute the free energy and the susceptibility of a q state potts model for arbitrary q on d dimensional hypercubic lattices the series are to order o 10 in the expansion variable nu ek 1 ek q 1 we show how to compute the expectation value of any operator on a finite graph for arbitrary number q of states of the potts model

stochastic versus possibilistic programming abstract we consider a linear program with uncertain parameters which are modeled as either random variables or as fuzzy variables we first construct the distribution of the optimal valve of the objective function to show a major difference between stochastic and possibilistic programming we then introduce a new solution concept where both programming problems are modeled as multiobjective games against nature

an extension to possibilistic linear programming abstract this paper proposes an extension to the solution of possibilistic linear programming problems with fuzzy number parameters introduced by buckley fuzzy sets and systems31 1989 329 341 the method relies on cuts of the fuzzy number parameters to generate a succession of pairs of classical linear programs the solutions of these linear programs produce a convex possibility distribution of the optimal objective values with the corresponding levels of the decision variables the approach is illustrated with an imprecise water quality management problem

an efficient method for the numerical solution of hammerstein mixed vf integral equations on 2d irregular domains abstract in this work we adapt the implicity linear collocation method for solving nonlinear two dimensional mixed volterra fredholm integral equations of hammerstein type by using imq rbfs on a non rectangular domain the proposed method is mesh free and it is independent of the geometry of domain convergence analysis of the proposed method together with some benchmark examples is provided which support its reliability and numerical stability

solving high order ordinary differential equations with radial basis function networks this paper is concerned with the application of radial basis function networks rbfns for numerical solution of high order ordinary differential equations odes two unsymmetric rbf collocation schemes namely the usual direct approach based on a differentiation process and the proposed indirect approach based on an integration process are developed to solve high order odes directly and the latter is found to be considerably superior to the former good accuracy and high rate of convergence are obtained with the proposed indirect method

numerical solution of integral equations by using combination of spline collocation method and lagrange interpolation abstract the numerical solutions to the nonlinear integral equations of the hammerstein type y t f t 0 1 k t s g s y s d s t 0 1 with using b splines functions are investigated an interpolation method based on b splines functions combined with a new collocation method is presented finally for showing efficiency of the method we give some numerical examples

fuzzy stochastic linear programming survey and future research directions in many real life problems one has to base decision on information which is both fuzzily imprecise and probabilistically uncertain although consistency indexes providing a union nexus between possibilistic and probabilistic representation of uncertainty exist there are no reliable transformations between them this calls for new paradigms for incorporating the two kinds of uncertainty into mathematical models fuzzy stochastic linear programming is an attempt to fulfill this need it deals with modelling and problem solving issues related to situations where randomness and fuzziness co occur in a linear programming framework in this paper we provide a survey of the essential elements methods and algorithms for this class of linear programming problems along with promising research directions being a survey the paper includes many references to both give due credit to results in the field and to help readers obtain more detailed information on issues of interest

solution of nonlinear volterra fredholm hammerstein integral equations via rationalized haar functions abstract rationalized haar functions are developed to approximate of the nonlinear volterra fredholm hammerstein integral equations the properties of rationalized haar functions are first presented and the operational matrix of integration together with the product operational matrix are utilized to reduce the computation of integral equations into some algebraic equations the method is computationally attractive and applications are demonstrated through illustrative examples

application of global optimization and radial basis functions to numerical solutions of weakly singular volterra integral equations a novel approach to the numerical solution of weakly singular volterra integral equa tions is presented using the cm multiquadric mq radial basis function rbf expansion rather than the more traditional finite difference finite element or polynomial spline schemes to avoid the collocation procedure that is usually ill conditioned we used a global minimization procedure combined with the method of successive approximations that utilized a small finite set of mq basis functions accurate solutions of weakly singular volterra integral equations are obtained with the minimal number of mq basis functions the expansion and optimization procedure was terminated whenever the global errors were less than 5 lo 2002 elsevier science ltd all rights reserved

variable transformations in the numerical solution of second kind volterra integral equations with continuous and weakly singular kernels extensions to fredholm integral equations abstract a number of techniques that use variable transformations in numerical integration have been developed recently cf sidi numerical integration iv h brass g hammerlin eds birkhauser basel 1993 pp 359 373 laurie j comput appl math 66 1996 337 344 the use of these transformations resulted in increasing the order of convergence of the trapezoidal and the midpoint quadrature rule in this paper the application of variable transformation techniques of sidi and laurie type to the numerical solution of second kind volterra integral equations with continuous and weakly singular kernels is considered since the transformations are such that the end points of integration need not be used as mesh points the methods introduced can be used for vie with both continuous and weakly singular kernel in a uniform way the methods have also the advantages of simplicity of application and of achieving high order of convergence the application of the idea to fredholm integral equations with continuous and weakly singular equations is also considered numerical results are included and they verify the expected increased order of convergence they were obtained by using the trapezoidal formula for the evaluation of the transformed integrals

a new spectral meshless radial point interpolation smrpi method for the two dimensional fredholm integral equations on general domains with error analysis in this article we present a numerical method to solve two dimensional fredholm integral equations of the second kind on general domains the method utilizes meshless and spectral collocation techniques but it is not traditional meshless collocation method the point interpolation method with the help of strictly positive definite radial basis functions is used to construct shape functions as a basis functions in the frame of spectral collocation methods these basis functions shape functions have kronecker delta function property since the proposed method is meshless it does not need any domain element and so it is independent of the geometry of the domain the method reduces the solution of the two dimensional integral equation to the solution of a linear system of algebraic equations convergence analysis with error estimates are given with full discussion furthermore some numerical examples are presented to show the validity and efficiency of smrpi

numerical solution of nonlinear volterra fredholm hammerstein integral equations via tau collocation method with convergence analysis in this paper we consider the nonlinear volterra fredholm hammerstein integral equations the approximate solution for the nonlinear volterra fredholm hammerstein integral equations is obtained by using the tau collocation method to do this the nonlinear volterra fredholm hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form thus by solving this system unknown coefficients are obtained the spectral rate of convergence for the proposed method is established in the l 2 norm the numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method the results show that the tau collocation method is of high accuracy more convenient and efficient for solving nonlinear volterra fredholm hammerstein integral equations

mathematical programming methods in the numerical solution of volterra integral and integro differential equations with weakly singular kernel abstract nonlinear volterra integral and integro differential equations with weakly singular kernel are considered and solved numerically using nonlinear mathematical programming methods based on minimax approximations in both cases polynomial and multiquadric approximation are used

adaptive numerical approach based upon chebyshev operational vector for nonlinear volterra integral equations and its convergence analysis abstract in the current paper we present a direct numerical scheme to approximate a second kind nonlinear volterra integral equations nvies the scheme is based upon shifted chebyshev polynomials and its operational matrices which eventually leads to the sparsity of the coefficients matrix of obtained system the main idea of the proposed approach is based on a useful property of chebyshev polynomials that yields to construct a new operational vector this vector eliminates any requirement of using projection methods and also enhances the accuracy vs other methods applied projection methods the constructive technique and the convergence analysis of this approach under the l w 2 norm are also described numerical experiments and comparisons confirm the applicability and the validity of the presented scheme

numerical solution of the nonlinear fredholm integral equations by positive definite functions a numerical method for solving the nonlinear fredholom integral equations is presented the method is based on interpolation by radial basis functions rbf to approximate the solution of the fredholm nonlinear integral equations several examples are given and numerical examples are presented to demonstrate the validity and applicability of the method

critical behavior of the random bond ashkin teller model a monte carlo study the critical behaviour of a bond disordered ashkin teller model on a square lattice is investigated by intensive monte carlo simulations a duality transformation is used to locate a critical plane of the disordered model this critical plane corresponds to the line of critical points of the pure model along which critical exponents vary continuously along this line the scaling exponent corresponding to randomness varies continuously and is positive so that randomness is relevant and different critical behaviour is expected for the disordered model we use a cluster algorithm for the monte carlo simulations based on the wolff embedding idea and perform a finite size scaling study of several critical models extrapolating between the critical bond disordered ising and bond disordered four state potts models the critical behaviour of the disordered model is compared with the critical behaviour of an anisotropic ashkin teller model which is used as a refference pure model we find no essential change in the order parameters critical exponents with respect to those of the pure model the divergence of the specific heat c is changed dramatically our results favor a logarithmic type divergence at tc c logl for the random bond ashkin teller and four state potts models and c log logl for the random bond ising model

bernoulli polynomials for the numerical solution of some classes of linear and nonlinear integral equations a new operational matrix for integration of bernoulli polynomials is introduced by using this new operational matrix of integration and the so called collocation method linear volterra and nonlinear volterra fredholm hammerstein integral equations are reduced to systems of algebraic equations with unknown bernoulli coefficients some error estimations are provided and illustrative examples are also included to demonstrate the efficiency and applicability of the technique a new operational matrix for integration of bernoulli polynomials is introduced a collocation method is used to reduce equations to systems of algebraic equations some error bounds and convergence results are provided for the proposed method the efficiency and applicability of the technique are checked by some examples

numerical solution of a class of mixed two dimensional nonlinear volterra fredholm integral equations using multiquadric radial basis functions an efficient numerical method is proposed for solving the mixed nonlinear volterra fredholm two dimensional integral equations ies using two dimensional radial basis functions rbfs this method is based on interpolation by radial basis functions including multiquadrics mqs using legendre gauss lobatto nodes and weights also a theorem is proved for convergence analysis some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method

water quality management with imprecise information abstract the application of fuzzy set and possibility theories for the representation of imprecise information in water quality management problems is investigated imprecision is associated with fuzziness which is non statistical in nature and refers to the absence of sharp boundaries in the information imprecise parameters in water quality decision making can be represented by possibility distributions defining maximum achievable probabilities the corresponding possibilistic programming problem is viewed as an alternative to the stochastic one where the parameters are modeled as fuzzy variables instead of random variables the possibilistic problem can be solved through a succession of classical linear programs the resulting possibility distributions of the objective value provide a possibilistic assessment of the risk based on possibility levels

a meshless discrete collocation method for the numerical solution of singular logarithmic boundary integral equations utilizing radial basis functions abstract the main intention of the current paper is to describe a scheme for the numerical solution of boundary integral equations of the second kind with logarithmic singular kernels these types of integral equations result from boundary value problems of laplace s equations with linear robin boundary conditions the method approximates the solution using the radial basis function rbf expansion with polynomial precision in the discrete collocation method the collocation method for solving logarithmic boundary integral equations encounters more difficulties for computing the singular integrals which cannot be approximated by the classical quadrature formulae to overcome this problem we utilize the non uniform composite gauss legendre integration rule and employ it to estimate the singular logarithm integrals appeared in the method since the scheme is based on the use of scattered points spread on the analyzed domain and does not need any domain elements we can call it as the meshless discrete collocation method the new algorithm is successful and easy to solve various types of boundary integral equations with singular kernels we also provide the error estimate of the proposed method the efficiency and accuracy of the new approach are illustrated by some numerical examples

revising the owa operator for multi criteria decision making problems under uncertainty abstract multi criteria decision making mcdm problems are usually under uncertainty one of these uncertain parameters is the decision maker dm s degree of optimism which has an important effect on the results fuzzy linguistic quantifiers are used to obtain the assessments of this parameter from dm and then because of its uncertainty it is assumed to have stochastic nature a new approach entitled fsrowa is introduced to combine the fuzzy and stochastic features into a revised owa operator if the dm is not aware of the risk in decision then the decision objective is to maximize the expected combined goodness measure if the dm cares only about the risk then minimizing the variance of the combined goodness measure is his her objective the results of the fsrowa provide the expected value and the variance of the combined goodness measure for each alternative in order to combine these two attributes a composite goodness measure is introduced this measure gives more robust decision outcomes the theoretical results are illustrated in a watershed management problem

high temperature series analysis of the free energy and susceptibility of the 2d random bond ising model abstract we derive high temperature series expansions for the free energy and susceptibility of the two dimensional random bond ising model with a symmetric bimodal distribution of two positive coupling strengths j1 and j2 and study the influence of the quenched random bond disorder on the critical behavior of the model by analysing the series expansions over a wide range of coupling ratios j2 j1 covering the crossover from weak to strong disorder we obtain for the susceptibility with two different methods compelling evidence for a singularity of the form t 7 4 ln t 7 8 as predicted theoretically by shalaev shankar and ludwig for the specific heat our results are less convincing but still compatible with the theoretically predicted log log singularity

a meshfree method for the numerical solution of the rlw equation in this paper we present a meshfree technique for the numerical solution of the regularized long wave rlw equation this approach is based on a global collocation method using the radial basis functions rbfs different kinds of rbfs are used for this purpose accuracy of the new method is tested in terms of l 2 and l error norms in case of non availability of the exact solution performance of the new method is compared with existing methods stability analysis of the method is established propagation of single and double solitary waves wave undulation and conservation properties of mass energy and momentum of the rlw equation are discussed

a meshless galerkin scheme for the approximate solution of nonlinear logarithmic boundary integral equations utilizing radial basis functions abstract this paper presents a computational scheme to solve nonlinear logarithmic singular boundary integral equations these types of integral equations arise from boundary value problems of laplace s equations with nonlinear robin boundary conditions the discrete galerkin method together with the inverse multiquadric radial basis functions established on scattered points is utilized to approximate the solution the discrete galerkin method for solving boundary integral equations results from the numerical integration of all integrals in the method the proposed scheme uses a special accurate quadrature formula via the nonuniform gauss legendre integration rule to compute logarithm like singular integrals appeared in the scheme since the numerical method developed in the current paper does not require any mesh generations on the boundary of the domain it is meshless and does not depend to the domain form we also investigate the error analysis of the proposed method illustrative examples show the reliability and efficiency of the new scheme and confirm the theoretical error estimates

a numerical solution of the nonlinear controlled duffing oscillator by radial basis functions in this research a new numerical method is applied to investigate the nonlinear controlled duffing oscillator this method is based on the radial basis functions rbfs to approximate the solution of the optimal control problem by using the collocation method we apply legendre gauss lobatto points for rbfs center nodes in order to use the numerical integration method more easily then the method of lagrange multipliers is used to obtain the optimum of the problems for this purpose different applications of rbfs are used the differential and integral expressions which arise in the dynamic systems the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients illustrative examples are included to demonstrate the validity and applicability of the technique

quenched bond dilution in two dimensional potts models we report a numerical study of the bond diluted two dimensional potts model using transfer matrix calculations for different numbers of states per spin we show that the critical exponents at the random fixed point are the same as in self dual random bond cases in addition we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin spin correlation function in the cylinder geometry we show that the behaviour is fully compatible with the one observed in the random bond case confirming the general picture according to which a unique fixed point describes the critical properties of different classes of disorder dilution self dual binary random bond self dual continuous random bond

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

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

the collocation method for hammerstein equations by daubechies wavelets the numerical solutions to the nonlinear integral equations of hammerstein typey t f t email protected 01k t s g s y s ds email protected 0 1 with using daubechies wavelets are investigated a general kernel scheme basing on daubechies wavelets combined with a collocation method is presented the approach of creating daubechies interval wavelets and their main properties are briefly mentioned also we present an algorithm for computing of daubechies wavelets in collocation points the rate of approximation solution converging to the exact solution is given finally we also give some numerical examples for showing efficiency of the method

the q state potts glass on d dimensional hypercubic lattices we use a high temperature star graph expansion to compute the free energy and the susceptibility of a q state potts glass with bimodal distribution of the random bonds the series are up to order o 20 in k beta j for arbitrary number of states q on d dimensional simple cubic lattices the result for the three state potts glass in three dimensions shows excellent consistency with existing monte carlo data

pseudospectral legendre based optimal computation of nonlinear constrained variational problems it is well known that spectrally accurate solution can be maintained if the grids on which a nonlinear physical problem is to be solved must be obtained by spectrally accurate techniques in this paper the pseudospectral legendre method for general nonlinear smooth and nonsmooth constrained problems of the calculus of variations is studied the technique is based on spectral collocation methods in which the trajectory x t is approximated by the nth degree interpolating polynomial using legendre gauss lobatto points as the collocation points and lagrange polynomials as trial functions the integral involved in the formulation of the problem is approximated based on legendre gauss lobatto integration rule thereby reducing the problem to a nonlinear programming one to which existing well developed algorithms may be applied the method is easy to implement and yields very accurate results illustrative examples are included to confirm the convergence of the pseudospectral legendre method moreover a numerical experiment on a nonsmooth problem indicates that by applying a smoothing filter procedure to the pseudospectral legendre approximation one can recover the nonsmooth solution within spectral accuracy

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

self consistent scaling theory for logarithmic correction exponents multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics here a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific heat critical exponent vanishes also the theory is widened to encompass the correlation function the new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made

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

spin models on random lattices under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a dierent behaviour than in the corresponding pure system here we discuss a series of monte carlo studies of a special type of such disordered systems namely spin models dened on quenched random lattices exhibiting geometrical disorder in the connectivity of the lattice sites in two dimensions we present results for the q state potts model on random tri valent 3 planar graphs which appear quite naturally in the dynamically triangulated random surface dtrs approach to quantum gravity as well as on poissonian random lattices of voronoi delaunay type both cases q64 and 4 are discussed which in the pure model without disorder give rise to second and rst order phase transitions respectively in three dimensions results for the ising model on poissonian random lattices are briey described we conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder and a discussion of the distinguishing dierences c 2000 elsevier science b v all rights reserved

a new collocation type method for hammerstein integral equations on presente une methode du type de collocation pour la resolution numerique des equations integrales d hammerstein on etablit la convergence de l approximation desiree vers la solution exacte

taylor polynomial solutions of nonlinear volterra fredholm integral equations the kanwal and liu method for the solution of fredholm integral equations is applied to certain nonlinear volterra fredholm integral equations in addition examples that illustrate the pertinent features of the method are presented and the results of study are discussed

adomian s method for hammerstein integral equations arising from chemical reactor theory an ordinary differential equation with a parameter in the boundary conditions describes the steady state in an adiabatic tubular chemical reactor in this paper the problem is considered as a hammerstein integral equation and solutions are obtained using adomian s decomposition method

application of fuzzy sets to aggregate production planning with multiproducts and multitime periods the objective of this study is to develop a fuzzy mathematical programming method to solve aggregate production planning app decision problems that involve multiproducts and multitime periods in a fuzzy environment the fuzzy app model that is developed here attempts to minimize total cost with respect to inventory carrying levels available labor levels machine capacity and warehouse space and the constraint of available budget the proposed app method evaluates monetary interest of related operating cost categories and provides greater computational efficiency and flexibility by adopting triangular fuzzy numbers and piecewise linear membership functions to represent both imprecise data and fuzzy goals the actual performance of an industrial company was used to demonstrate the feasibility of applying the proposed method to real world app decisions the proposed method yields an efficient solution and presents overall decision maker satisfaction with the given goal values this paper also presents several significant management implications that are related to the practical application of the proposed method

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

application of the multiquadric method for numerical solution of elliptic partial differential equations abstract we have used the multiquadric mq approximation scheme for the solution of elliptic partial differential equations with dirichlet and or neumann boundary conditions the scheme has the advantage of using the data points in arbitrary locations with an arbitrary ordering two dimensional laplace poisson and biharmonic equations describing the various physical processes have been taken as the test examples the agreement is found to be very good between the computed and exact solutions the method also provides an excellent approximation with a curved boundary

the parameter r2 in multiquadric interpolation the multiquadric mq method is an effective bivariate interpolant to three dimensional data xi yi zi where the xi yi are arbitrarily located in the plane the accuracy of the mq method is dependent on a user defined parameter r2 and most practitioners select r2 based upon the number of data points and the locations of the xi yi in the plane we observe that the optimal value of r2 is a strong function of the zi and that it is essentially independent of both the number and the locationsof the xi yi points contrary to some opinions we observe that the mq method can effectively interpolate to track data that is data sampled densely along tracks in the plane together with several other observations we present an algorithm that generally yields an effective value for r2

an efficient algorithm for solving nonlinear volterra fredholm integral equations in this work we develop a new effective method for solving nonlinear volterra fredholm integral equation the existence of any e approximate solution is proved at the same time an effective method for obtaining the e approximate solution is established the final numerical examples illustrate that our approach is valid not only for weakly nonlinear problems but also for strongly nonlinear problems

a meshless method for solving nonlinear two dimensional integral equations of the second kind on non rectangular domains using radial basis functions with error analysis in this paper we present a numerical method for solving two dimensional nonlinear fredholm integral equations of the second kind on a non rectangular domain the method utilizes radial basis functions rbfs constructed on scattered points as a basis in the discrete collocation method the proposed scheme is meshless since it does not need any domain element and so it is independent of the geometry of the domain the method reduces the solution of the two dimensional nonlinear integral equation to the solution of a nonlinear system of algebraic equations error analysis is presented for this method finally numerical examples are included to show the validity and efficiency of the new technique

joint solution to fuzzy programming problems we propose a new solution concept for fuzzy programming problems it is based on our new method of solving fuzzy equations 101 for simplicity we discuss in detail only fuzzy linear programming in this paper we define and obtain the basic properties of the joint solution a fuzzy vector in rn and the optimal value of the objective function a fuzzy number three examples are presented illustrating these concepts

numerical solution of the nonlinear klein gordon equation using radial basis functions the nonlinear klein gordon equation is used to model many nonlinear phenomena in this paper we propose a numerical scheme to solve the one dimensional nonlinear klein gordon equation with quadratic and cubic nonlinearity our scheme uses the collocation points and approximates the solution using thin plate splines tps radial basis functions rbf the implementation of the method is simple as finite difference methods the results of numerical experiments are presented and are compared with analytical solutions to confirm the good accuracy of the presented scheme