in this paper, we will compare a homotopy perturbation algorithm and taylor series expansin method for a system of second kind fredholm integral equations. an application of he’s homotopy perturbation method is applied to solve the system of fredholm integral equations. taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

We present numerical schemes for the strong solution of linear stochastic differential equations driven by an arbitrary number of Wiener processes. These schemes are based on the Neumann (stochastic Taylor) and Magnus expansions. Firstly, we consider the case when the governing linear diffusion vector fields commute with each other, but not with the linear drift vector field. We prove that nume...

We present a decomposition algorithm to solve a multi-level large scale quadratic programming problem with stochastic parameters in the objective functions. In the first phase of the solution algorithm and to avoid the complexity of this problem, the stochastic nature of the problem is converted into the equivalent crisp problem. In the second phase, Taylor series is combined with a decompositi...

Most available integration techniques for stochastically driven engineering dynamical systems are based on stochastic Taylor expansions of the response variables and thus require numerical modelling of multiple stochastic integrals (MSI-s). Since the latter is an extremely involved numerical task and becomes inaccurate for higher level MSI-s, these methods fail to achieve an accuracy beyond a l...

This letter is concerned with solving continuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In proposed method, we apply TME method to approximate transition density of stochastic differential equation in dynamic model. Furthermore, derive a theoretical error bound (in mean square sense) estimates showing that smoother stable under weak assumptions. ...

this paper presents a class of theoretical and iterative method for linear partial differential equations. an algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. in this technique, the solution is calculated in the form of a series with easily computable components. there test modeling problems from mathematical mechanic, physi...