the approximation for the boundary optimal control problem of burgers fisher equation with constraints this paper deals with the numerical approximation with meshless method for the boundary optimal control problem with some control and state constraints governed by the burgers fisher equation which is a nonlinear evolution equation and is the prototype model for the reaction convection and diffusion phenomena arising in many spatial temporal processes by making use of the element free galerkin efg method the original optimal control problem is discretized spatially to a semi discrete optimal control problem governed by a system of nonlinear ordinary differential equations then by using the control parameterization method the original problem can be reduced to an optimal parameter selection problem governed by a lumped parameter system which can be solved as a nonlinear optimization problems by using the sequential quadratic programming sqp algorithm the numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method

application of homotopy perturbation method for solving eighth order boundary value problems homotopy perturbation method is applied to the numerical solution for solving eighth order boundary value problems comparison of the result obtained by the present method with that obtained by modified decomposition method m mesrovic the modified decomposition method for eighth order boundary value problems appl math comput 2006 doi 10 1016 j amc 2006 11 015 reveals that the present method is very effective and convenient

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

an exponential time differencing method of lines for burgers fisher and coupled burgers equations abstract an exponential time differencing scheme using the method of lines is developed in this article for the numerical solution of the generalized burgers fisher and coupled burgers equations in each of the aforementioned cases the resulting nonlinear systems are solved explicitly using a second order modified predictor corrector method the efficiency of the method introduced is tested by comparing our experimental results with others selected from the available literature

a note on the adomian decomposition method for the generalized huxley equation in a recent paper ismail et al adomian decomposition method for burgers huxley and burgers fisher equations appl math comput 159 2004 291 301 employed the adomian decomposition method adm to solve in particular a generalized nonlinear huxley equation the purpose of this note is to correct ismail et al s numerical solutions of the generalized huxley equation in addition a convergence proof of the adm applied to the generalized huxley equation is also given

a numerical solution for solving system of fredholm integral equations by using homotopy perturbation method abstract homotopy perturbation method is applied to the numerical solution for solving system of fredholm integral equations comparison of the result obtained by the present method with that obtained by taylor series expansion method k maleknejad n aghazade m rabbani numerical solution of second kind fredholm integral equations system by using a taylor series expansion method appl math comput 175 2006 1229 1234 reveals that the present method is very effective and convenient

stochastic nonlinear schrodinger equation on an upper right quarter plane with dirichlet random boundary in this paper we study the nonhomogeneous stochastic initial boundary value problem for the nonlinear schrodinger equation on an upper right quarter plane with random dirichlet boundary conditions the main novelty of this work is a convenient framework for the analysis of such equations excited by the wiener additive noise on the boundary our approach allows us to show the local existence and uniqueness of solutions in the space h2 the basic properties of the solutions such as the continuity and the boundary layer behavior are also studied using the ito calculus despite several technical difficulties we believe that the approach developed in this paper can be applied to the case of a large class of noise including fractional wiener space time white noise homogeneous noise and levy noise

an explicit and numerical solutions of some fifth order kdv equation by decomposition method in this paper by considering the adomian decomposition method explicit and numerical solutions are calculated for a various fifth order korteweg de vries equations with initial condition the method does not need linearization or weak nonlinearity assumptions perturbation theory the decomposition series explicit solution of the equation is quickly obtained by observing the existence of the self canceling noise terms where sum of components vanishes in the limit

solitary wave solutions for a generalized hirota satsuma coupled kdv equation the solitary wave solutions of a generalized hirota satsuma coupled kdv equation are obtained exactly by using the decomposition method the solutions were calculated in the form of a convergent power series with easily computable components a variety of initial value system is considered the convergence of the method as applied to the coupled kdv equation is illustrated numerically the present algorithm performs extremely well in terms of accuracy and simplicity

spectral collocation method for the solution of the generalized burger fisher equation abstract in this paper we present a new method for solving the generalized burger fisher equation by using the collocation formula for calculating spectral differentiation matrix for chebyshev gauss lobatto point firstly theory of application of pseudospectral method on burger fisher equations is presented this method yields burger fisher equation to a system of ordinary differential equations odes secondly we use forth order runge kutta formula for the numerical integration of the system of ode the numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method

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

a numerical solution of the generalized burger s huxley equation by spectral collocation method abstract in this paper we present a new method for solving of the generalized burger s huxley equation by using the collocation formula for calculating spectral differentiation matrix for chebyshev gauss lobatto points firstly theory of application of pseudospectral method on burger s huxley equations presented this method yields burger s huxley equation to a system of ordinary differential equations odes secondly we use fourth order runge kutta formula for the numerical integration of the system of ode the numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method

conditional symmetries and riemann invariants for hyperbolic systems of pdes this paper contains an analysis of rank k solutions in terms of riemann invariants obtained from interrelations between two concepts that of the symmetry reduction method and of the generalized method of characteristics for first order quasilinear hyperbolic systems of pdes in many dimensions a variant of the conditional symmetry method for obtaining this type of solutions is proposed a lie module of vector fields which are symmetries of an overdetermined system defined by the initial system of equations and certain first order differential constraints is constructed it is shown that this overdetermined system admits rank k solutions expressible in terms of riemann invariants finally examples of applications of the proposed approach to the fluid dynamics equations in k 1 dimensions are discussed in detail several new soliton like solutions among them kinks bumps and multiple wave solutions have been obtained these solutions remain bounded even when the riemann invariants admit a gradient catastrophe some physical interpretation of these results is discussed

numerical solution of burgers fisher equation by cubic b spline quasi interpolation abstract in this paper numerical solution of the burgers equation is presented based on the cubic b spline quasi interpolation at first the cubic b spline quasi interpolation is introduced moreover the numerical scheme is presented by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable the accuracy of the proposed method is demonstrated by some test problems the numerical results are found in good agreement with exact solutions the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement

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

adomian decomposition method for solving fractional nonlinear differential equations in this article we have discussed a new application of adomian decomposition method on time fractional nonlinear fractional differential equations three models with fractional time derivative of order a 0 a 1 are considered and solved by means of adomian decomposition method the behaviour of adomian solutions and the effects of different values of a are investigated numerical examples are tested to illustrate the pertinent feature of the proposed algorithm

a numerical simulation and explicit solutions of the generalized burgers fisher equation we consider solitary wave solutions of the generalized burgers fisher bf equation u t pu ru x u x x qu 1 u r 0 in this paper by considering the decomposition scheme we first obtain the exact solutions of the generalized bf equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of some values r 2 of the generalized bf equation

construction of a solitary wave solution for the generalized zakharov equation by a variational iteration method in this paper the well known he s variational iteration method vim is used to construct solitary wave solutions for the generalized zakharov equation gze the chosen initial solution trial function can be in soliton form with some unknown parameters which can be determined in the solution procedure

adaptive numerical method for burgers type nonlinear equations abstract in this paper a moving mesh partial differential equation mmpde approach will be applied to some types of nonlinear partial differential equations the method is described in detail and a number of computational examples are presented using different monitor functions applied to the burgers type equations

a variational iteration method for solving parabolic partial differential equations in this paper he s variational iteration method is employed successfully for solving parabolic partial differential equations with dirichlet boundary conditions in this method the solution is calculated in the form of a convergent series with an easily computable component this approach does not need linearization weak nonlinearity assumptions or perturbation theory the results reveal that the method is very effective and convenient

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

exact and numerical traveling wave solutions of whitham broer kaup equations in this paper we find the explicit and numerical traveling wave solutions of whitham broer kaup for short wbk equations which contain blow up solutions and periodic solutions by using the decomposition method by using this method the solutions were calculated in the form of a convergent power series with easily computable components the convergence of the method as applied to the whitham broer kaup equations is illustrated numerically