in this paper, the variational iteration method proposed by ji-huan he is applied to solve both linear and nonlinear schrodinger equations. the main property of the method is in its flexibility and ability to solve linear and nonlinear equations accurately and conveniently. in this method, general lagrange multipliers are introduced to construct correction functionals to the problems. the multi...

duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

in this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear volterra integral equations of the first-kind is proposed. this problem is transformedto a nonlinear two-dimensional volterra integral equation of the second-kind. the properties ofthe bivariate shifted legendre functions are presented. the operational matrices of integrationtogether with the produ...

sufficient conditions are established under which the zero solution x = 0 of equation (2) isunstable.

solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modi ed korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

in this article we study steensen method to solve nonlinear matrix equation x+a^t x^(-1) a=q, when a is a normal matrix. we establish some conditions that generate a sequence of positive de nite matrices which converges to solution of this equation.

this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

the numerical methods are of great importance for approximating the solutions of nonlinear ordinary or partial differential equations, especially when the nonlinear differential equation under consideration faces difficulties in obtaining its exact solution. in this latter case, we usually resort to one of the efficient numerical methods. in this paper, the chebyshev collocation method is sugge...