solution of boundary value problems for integro differential equations by using differential transform method in this study we extended the differential transform method dtm to solve the integro differential equations new theorems for the transformation of integrals are introduced and prooved the commonly encountered linear and nonlinear integro differential equations that appear in literature are solved as an illustration for the efficiency of the method some numerical results are also given to demonstrate the superiority of the method to other common techniques the results we obtained by using this technique is much more accurate compared to the existing ones

dynamics of the deterministic and stochastic siqs epidemic model with non linear incidence the deterministic and stochastic siqs models with non linear incidence are introduced for deterministic model the basic reproductive rate r 0 is derived moreover if r 0 1 there exists a unique endemic equilibrium which is globally asymptotically stable for stochastic model sufficient condition for extinction of the disease that is regardless of the value of r 0 is presented in addition if the intensities of the white noises are sufficiently small and r 0 1 then there exists a unique stationary distribution to stochastic model numerical simulations are also carried out to confirm the analytical results

applications of differential transform method to differential algebraic equations in this paper numerical solution of linear differential algebraic equations daes is considered by differential transform method two different problems have been solved by using the technique and solutions have been compared very well with those obtained by exact solutions differential transform method can easily be applied to daes and series solutions are obtained after the transformation here we have formulated series coefficients very simply for the considered problems

dynamics in a stochastic heroin model with seasonal variation abstract in this paper a stochastic non autonomous heroin model is formulated we obtain sufficient conditions for extinction and permanence in mean with probability one of the positive solutions in addition we prove that there exists at least one positive periodic solution under some conditions finally numerical simulations are performed to illustrate our theoretical results

on the two dimensional differential transform method in this paper two dimensional differential transform method of solution of the initial value problem for partial differential equations pdes have been studied new theorems have been added and some linear and nonlinear pdes solved by using this method the method can be easily applied to linear or nonlinear problems and is capable of reducing the size of computational work in this work additionally analytical form solutions of two diffusion problems have been obtained and the solutions are compared very well with those obtained by decomposition method

a novel semi analytical approach for solving nonlinear volterra integro differential equations in this work we present an efficient semi analytical method based on the taylor series for solving nonlinear volterra integro differential equations namely the differential transform method dtm the dtm provides a recursive relation for the coefficients of the taylor series that is derived from the given equations we provide a new recursive relation for the nonlinear volterra integro differential equations with complex nonlinear kernels since the dtm is based on the taylor series it is difficult to obtain accurate approximate solutions in a large domain to overcome this difficulty the standard dtm is applied in each subdomain called the multistage differential transform method msdtm we also present an convergence analysis for the proposed method to demonstrate the efficiency of the proposed method several numerical examples are performed and support the results in our analysis

solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method in this paper we will give some results for developing the two dimensional differential transform tddt for double integrals then the tddt method will be developed for solving a class of two dimensional linear and nonlinear volterra integral equations we also give some examples to demonstrate the accuracy of the method

a computational method for solving a class of two dimensional volterra integral equations the use of the geometric series theorem together with schauder bases in certain banach spaces allows us to design a numerical algorithm in order to solve an important type of two dimensional linear integral equations a study of the convergence and error is presented here all the calculations can be easily implemented and the efficiency of this method will be shown with numerical results

a note on a modified simplex approach for solving bilevel linear programming problems abstract we analyze the article a modified simplex approach for solving bilevel linear programming problems ejor 67 126 135 we point out some problems in its theoretical analysis moreover the algorithm proposed may not find a global solution as it is claimed we give some examples in order to illustrate these remarks

solutions of the system of differential equations by differential transform method in this study three dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time moreover as an application of two and three dimensional differential transform exact solutions of linear and non linear systems of partial differential equations have been investigated the results of the present method are compared very well with those obtained by decomposition method differential transform method can easily be applied to linear or non linear problems and reduces the size of computational work with this method exact solutions may be obtained without any need of cumbersome work and it is an useful tool for analytical and numerical solutions

stochastic analysis of a novel nonautonomous periodic siri epidemic system with random disturbances abstract in this paper a new stochastic nonautonomous siri epidemic model is formulated given that the incidence rates of diseases may change with the environment we propose a novel type of transmission function the main aim of this paper is to obtain the thresholds of the stochastic siri epidemic model to this end we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable lyapunov functions and using stochastic analysis technique furthermore we show that the stochastic system has at least one nontrivial positive periodic solution finally numerical simulations are introduced to illustrate our results

modelling the effect of telegraph noise in the sirs epidemic model using markovian switching abstract we discuss the effect of introducing telegraph noise which is an example of an environmental noise into the susceptible infectious recovered susceptible sirs model by examining the model using a finite state markov chain mc first we start with a two state mc and show that there exists a unique nonnegative solution and establish the conditions for extinction and persistence we then explain how the results can be generalised to a finite state mc the results for the sir susceptible infectious removed model with markovian switching ms are a special case numerical simulations are produced to confirm our theoretical results

numerical solutions of nonlinear two dimensional partial volterra integro differential equations by haar wavelet a non linear kernel comprising a function of partial derivatives of arbitrary order is approximated by theorem 2 in ref 12 after substituting the kernel approximation in the original equation a nonlinear system is obtained using the haar wavelet solving the nonlinear system the nonlinear two dimensional integro differential volterra equation with partial derivatives is converted to a simple equation containing partial derivatives solving this simple equation we can approximate the solution of the nonlinear two dimensional integro differential volterra equation

a fuzzy approach for bi level integer non linear programming problem abstract bi level programming a tool for modeling decentralized decisions consists of the objective of the leader at its first level and that is of the follower at the second level integer programming deals with the mathematical programming problems in which some or all the variables are to be integer this paper studies a bi level integer non linear programming problem with linear or non linear constraints and in which the non linear objective function at each level are to maximized the bi level integer non linear programming bli nlp problem can be thought as a static version of the stackelberg strategy which is used leader follower game in which a stackelberg strategy is used by the leader or the higher level decision maker hldm given the rational reaction of the follower or the lower level decision maker lldm this paper proposes a two planner integer model and a solution method for solving this problem this method uses the concept of tolerance membership function and the branch and bound technique to develop a fuzzy max min decision model for generating pareto optimal solution for this problem an illustrative numerical example is given to demonstrate the obtained results

a stochastic differential equation sis epidemic model in this paper we extend the classical susceptible infected susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation sde for the number of infectious individuals i t we then prove that this sde has a unique global positive solution i t and establish conditions for extinction and persistence of i t we discuss perturbation by stochastic noise in the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance the results are illustrated by computer simulations including two examples based on real life diseases

sde sis epidemic model with demographic stochasticity and varying population size an sde sis epidemic model with demographic stochasticity is developed existence of a unique non negative solution is shown an upper bound is found for the infectives in terms of the population size the infectives and susceptibles go extinct in finite time a s results are supported numerically some with real examples in this paper we look at the two dimensional stochastic differential equation sde susceptible infected susceptible sis epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size first we look at the sde model for the total population size and show that there exists a unique non negative solution then we look at the two dimensional sde sis model and show that there exists a unique non negative solution which is bounded above given the total population size furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely lastly we support our analytical results with numerical simulations using theoretical and realistic disease parameter values

richardson extrapolation of iterated discrete galerkin solution for two dimensional fredholm integral equations in this paper we study the numerical solution of two dimensional fredholm integral equation by discrete galerkin and iterated discrete galerkin method we are able to derive an asymptotic error expansion of the iterated discrete galerkin solution this expansion covers arbitrarily high powers of the discretization parameters if the solution of the integral equation is smooth the expansion gives rise to richardson type extrapolation schemes which rapidly improve the original rate of the convergence numerical experiments confirm our theoretical results

on solving the initial value problems using the differential transformation method in this paper initial value problems are solved by the differential transformation method the differential transformation method of fixed grid size is used to approximate solutions of linear and nonlinear initial value problems an adaptive grid size mechanism based on the fixed grid size technique is also proposed the proposed adaptive grid size procedure provides concise adjustment policy and raises computational efficiency of using differential transformation method

comments on solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method tari et al a tari m y rahimi s shahmorad f talati solving a class of two dimensional linear and nonlinear volterra integral equations by the differential transform method j comput appl math 228 2009 70 76 presented some fundamental properties of tdtm for the kernel functions in two dimensional volterra integral equations here we suggest simple proofs of those fundamental properties by using the basic properties of tdtm furthermore we present some fundamental properties of tdtm for the kernel functions of a quotient type in two dimensional volterra integral equations numerical illustrations are demonstrated to show the effectiveness of the tdtm for solving two dimensional volterra integral equations

solving partial differential equations by two dimensional differential transform method using two dimensional differential transform to solve partial differential equations pde is proposed in this study first the theory of two dimensional differential transform is introduced second taking two dimensional differential transform of a pde problem a set of difference equations is derived doing some simple mathematical operations on these equations we can get a closed form series solution or an approximate solution quickly finally three pde problems with constant and variable coefficients are solved by the present method the calculated results are compared very well with those obtained by other analytical or approximate methods

stochastic permanence of an siqs epidemic model with saturated incidence and independent random perturbations abstract this article discusses a stochastic siqs epidemic model with saturated incidence we assume that random perturbations always fluctuate at the endemic equilibrium the existence of a global positive solution is obtained by constructing a suitable lyapunov function under some suitable conditions we derive the stochastic boundedness and stochastic permanence of the solutions of a stochastic siqs model some numerical simulations are carried out to check our results

the threshold of a stochastic delayed sir epidemic model with temporary immunity abstract this paper is concerned with the asymptotic properties of a stochastic delayed sir epidemic model with temporary immunity sufficient conditions for extinction and persistence in the mean of the epidemic are established the threshold between persistence in the mean and extinction of the epidemic is obtained compared with the corresponding deterministic model the threshold affected by the white noise is smaller than the basic reproduction number r 0 of the deterministic system

two dimensional differential transform for partial differential equations the differential transform is a numerical method for solving differential equations in this paper we present the definition and operation of the two dimensional differential transform a distinctive feature of the differential transform is its ability to solve linear and nonlinear differential equations partial differential equation of parabolic hyperbolic elliptic and nonlinear types can be solved by the differential transform we demonstrate that the differential transform is a feasible tool for obtaining the analytic form solutions of linear and nonlinear partial differential equation

a modified simplex approach for solving bilevel linear programming problems abstract a method for solving bilevel linear programming problems is proposed the inner problem is represented by its kuhn tucker conditions and the complementary slackness equations are moved to the outer objective as a penalty function the global optimum of the resulting quadratic programme is reached by iterative application of a modified simplex algorithm

dynamics for a class of stochastic sis epidemic models with nonlinear incidence and periodic coefficients abstract in this paper we investigate the dynamics of a class of periodic stochastic sis epidemic models with general nonlinear incidence f s i some sufficient conditions on the permanence in the mean and extinction of positive solutions with probability one are established by using the khasminskii s boundary periodic markov processes the existence of stochastic nontrivial periodic solution for the models is also obtained the numerical simulations are given to illustrate the main theoretical results and some interesting conjectures are presented

the threshold of a stochastic sivs epidemic model with nonlinear saturated incidence abstract a stochastic version of the sis epidemic model with vaccination sivs is studied when the noise is small the threshold parameter is identified which determines the extinction and persistence of the epidemic besides the results show that large noise will suppress the epidemic from prevailing regardless of the saturated incidence the results are illustrated by computer simulations