this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...

In this paper we demonstrate that a number of fixed point iteration problems can be solved using a modified Krasnoselskij iteration process, which is much simpler to use than the other iteration schemes that have been defined. 2008 Elsevier Inc. All rights reserved. For maps with a slow enough growth rate, the Banach contraction principle provides the existence and uniqueness of the fixed point...

A new method of constructing elliptic finite-gap solutions of the stationary Korteweg-de Vries (KdV) hierarchy, based on a theorem due to Picard, is illustrated in the concrete case of the Lamé-Ince potentials −s(s+1)P(z), s ∈ N (P(.) the elliptic Weierstrass function). Analogous results are derived in the context of the stationary modified Korteweg-de Vries (mKdV) hierarchy for the first time.

In this short note, we study the local well-posedness of a 3D model for incompressible Navier-Stokes equations with partical viscosity. This model was originally proposed by Hou-Lei in [4]. In a recent paper, we prove that this 3D model with partial viscosity will develop a finite time singularity for a class of initial condition using a mixed Dirichlet Robin boundary condition. The local well-...

This paper evaluates the performance of multiphysics coupling algorithms on a light water nuclear reactor core simulation. The simulation couples the k-eigenvalue form of the neutron transport equation with heat conduction and subchannel flow equations. We compare Picard iteration (block GaussSeidel) with multiple variants of preconditioned Jacobian-free Newton-Krylov (JFNK). The performance of...

The popular fuzzy c-means algorithm (FCM) converges to a local minimum of the objective function. Hence, different initializations may lead to different results. The important issue is how to avoid getting a bad local minimum value to improve the cluster accuracy. The particle swarm optimization (PSO) is a popular and robust strategy for optimization problems. But the main difficulty in applyin...

This paper presents a new feedback-accelerated Picard iteration method for solving long-term orbit-propagation problemsandperturbedLambert’s problems.Thismethod is developedby combining the collocationmethodand the variational iterationmethod over large time steps. The resulting iterative formulas are explicitly derived so that they canbedirectly adopted to solve problems in orbitalmechanics. S...

Dynamic iteration methods for treating linear systems of diierential equations are considered. It is shown that the discretized Picard-Lindell of (waveform relaxation) iteration can be accelerated by solving the defect equations with a larger timestep, or by using a recursive procedure based on a succession of increasing timesteps. A discussion of convergence is presented, including analysis of...