In this paper, a new approach to the variational iteration method is introduced to solve systems of first-order differential equations. Since higher-order differential equations can almost always be converted into a first-order system of equations, the proposed method is still applicable to a wide range of differential equations. This generalised approach, unlike the classical method, uses rest...

-Using the He’s variational iteration method, it is possible to find the exact solutions or better approximate solutions of the partial differential equations. In this method, a correction functional is constructed by a general Lagrange multiplier, which can be identified via variational theory. In this paper, this method is used for solving a nonlinear partial differential equation, a three-di...

this paper gives an ecient numerical method for solving the nonlinear systemof volterra-fredholm integral equations. a legendre-spectral method based onthe legendre integration gauss points and lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

the main purpose of this article is to increase the efficiency of the least squares method in numerical solution of ill-posed functional and physical equations. determining the least squares of a given function in an arbitrary set is often an ill-posed problem. in this article, by defining artificial constraint and using lagrange multipliers method, the attempt is to turn -dimensional least squ...

In recent years, parallel computers have changed techniques to solve problems in various kinds of fields. In parallel computers of distributed memory type, data can be shared by communication procedures called message-passing, whose speed is slower than that of computations in a processor. From a practical point of view, it is important to reduce the amount of message-passing. Domain-decomposit...

The alternating direction method of multipliers (ADMM) is an application of the Douglas-Rachford splitting method; and the symmetric version of ADMM which updates the Lagrange multiplier twice at each iteration is an application of the Peaceman-Rachford splitting method. Sometimes the symmetric ADMM works empirically; but theoretically its convergence is not guaranteed. It was recently found th...

This paper reformulates a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions, called complex Fourier hereafter, for solving two-dimensional elastodynamic problems. These shape functions, which are derived from their corresponding radial basis functions, have some advantages such as the satisfaction of exponential and trigonometric function fields in comple...

The optimized Schwarz method and the closely related 2-Lagrange multiplier method are domain decomposition methods which can be used to parallelize the solution of partial differential equations. Although these methods are known to work well in special cases (e.g., when the domain is a square and the two subdomains are rectangles), the problem has never been systematically stated nor analyzed f...

A quadratic programming problem with positive definite Hessian and bound constraints is solved, using a Lagrange multiplier approach. The proposed method falls in the category of exterior point, active set techniques. An iteration of our algorithm modifies both the minimization parameters in the primal space and the Lagrange multipliers in the dual space. Comparative results of numerical experi...

in this paper, we use petrov-galerkin elements such as continuous and discontinuous lagrange-type k-0 elements and hermite-type 3-1 elements to find an approximate solution for linear fredholm integro-differential equations on $[0,1]$. also we show the efficiency of this method by some numerical examples