1 Abstract — This paper presents a potential algorithm for continuation power flow method in voltage stability assessment. Modified continuation power flow method termed as MCBF was developed which solved the solution of bifurcation point at the Q-V curve. The solvability of power flow at the bifurcation point beyond the maximum loadability point of a system was achieved through the implementat...

In this paper, we propose a continuation method for box constrained variational inequality problems. The continuation method is based on the class of Gabriel-Mor e smooth functions and has the following attractive features: It can start from any point; It has a simple and natural neighborhood deenition; It solves only one approximate Newton equation at each iteration; It converges globally line...

This paper contains a computational approximation for the solution of a forward-backward differential equation that models nerve conduction in a myelinated axon. We look for a solution of an equation defined in R, which tends to known values at ±∞. Extending the approach introduced in [5, 10, 6] for linear case, a numerical method for the solution of problem, is adapted to non linear case using...

We consider the initial boundary value problem for the homogeneous heat equation, with homogeneous Dirichlet boundary conditions. By the maximum principle the solution is nonnegative for positive time if the initial data are nonnegative. We study to what extent this property carries over to some piecewise linear finite element discretizations, namely the Standard Galerkin method, the Lumped Mas...

The partial di erential equations describing the evolution of thin liquid lms on solid substrates in lubrication approximation are highly non-linear. Thus, the classical semi-implicit time integrator with a constant linear part fails due to a strong variation of the Jacobian between two consecutive time-steps. We propose to integrate the equations using an exponential propagation. This method r...

Abstract A new fast and efficient algorithm for the solution of the dynamic optimization problem resulted from the implementation of a model predictive control (MPC) framework in highly nonlinear dynamic systems is presented. The sequence of the optimal control actions is obtained through the solution of the parameterized set of the Karush-KuhnTucker (KKT) optimality conditions for the nonlinea...

A generalized optimization problem in which design space is also a design to be found is de9ned and a numerical implementation method is proposed. In conventional optimization, only a portion of structural parameters is designated as design variables while the remaining set of other parameters related to the design space are often taken for granted. A design space is speci9ed by the number of d...

We study the discrete nonlinear Schrödinger (DNLS) equations that model rotating Bose-Einstein Condensates (BEC) both analytically and numerically. Due to the difficulties associated with transformation invariant solutions, standard continuation methods may not properly follow the solution curves of the DNLS equations. We propose a quotient transformation invariant continuation method to circum...

We present a set of C++ classes that realize an abstract inexact Gauss Newton method in combination with a continuation process for the solution of parameter dependent nonlinear problems. The object oriented approach allows the continuation of diierent types of solutions within the same framework.

In this paper we compare diierent continuation methods for the searching of periodic orbits of the Froeschl e map, which is a four dimensional symplectic map. We nd relations between the stability of the periodic orbits and the problem to solve the system given in the continuation method.