this paper presents a framework for long term transmission expansion planning in competitive, electricity markets. transmission lines and phase shifters are taken into account as expansion options. maximization of the network users' benefits, with satisfying security constraints are considered as the criterion for transmission expansion planning. the elements of the objective function are the...

ADER schemes are numerical methods, which can reach an arbitrary order of accuracy in both space and time. They are based on a reconstruction procedure and the solution of generalized Riemann problems. However, for general boundary conditions, in particular of Dirichlet type, a lack of accuracy might occur if a suitable treatment of boundaries conditions is not properly carried out. In this wor...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

The optimal control of a spacecraft as it transitions between specified states using continuous thrust in a fixed amount of time is studied using a recently developed technique based on Hamilton–Jacobi theory. Started from the first-order necessary conditions for optimality, a Hamiltonian system is derived for the state and adjoints with split boundary conditions. Then, with recognition of the ...

The modified (w/g)-expansion method for finding traveling wave solutions of nonlinear evolution equations is presented in this paper, which can be thought of as the generalization of the well-known (G′/G)-expansion method given recently by Wang et al. When the w and g are taken special choices, some familiar expansion methods can be obtained. Based on these interesting results, we further give ...

In this paper a generalized tanh-function type method is proposed by using the idea of the transformed rational function method. We show that the G G  -expansion method is a special case of the generalized tanh-function type method, so the G G   -expansion method is considered as a special deformation application of the transformed rational function method. We demonstrate that all solutio...