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...

and Applied Analysis 3 in 1.3 plays the role of a ”perturbation term” and its choice is, of course, not unique. The solution of problem 1.3 is sought for in an analytic form by the method of successive approximations similar to the Picard iterations. According to the formulas

A general method is developed to obtain conditions on initial data and forcing terms for the global existence of unique regular solutions to incompressible 3d Navier-Stokes equations. The basic idea generalizes a probabilistic approach introduced by LeJan and Sznitman (1997) to obtain weak solutions whose Fourier transform may be represented by an expected value of a stochastic cascade. A funct...

In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature, from modelling pattern formation in developmental biology to cancer research, wound healing, tissue and bone regeneration and cell motility. Therefore, it is...

In this paper, we introduce a modification of the Picard iteration method (PIM) using Padé approximation and so called Picard-Padé technique. Special attention is given to study the convergence analysis of the proposed method. Convergence analysis is reliable enough to estimate the maximum absolute error of the solution given by PIM. A basic enzyme kinetics is used to test the effectiveness of ...