This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for incompressible Navier-Stokes equations, where we restrict our attention to $O(1)$ parameter, and Anderson acceleration (AA) is used significantly improve its convergence properties. After showing fixed point operator associated with IPP iteration Lipschitz continuous continuously (Frechet) differentiab...

This paper considers an enhancement of the classical iterated penalty Picard (IPP) method for incompressible Navier-Stokes equations, where we restrict our attention to $O(1)$ parameter, and Anderson acceleration (AA) is used significantly improve its convergence properties. After showing fixed point operator associated with IPP iteration Lipschitz continuous continuously (Frechet) differentiab...

In this work, we study the exponential stability of stationary distribution a McKean-Vlasov equation, nonlinear hyperbolic type which was recently derived in [1], [2]. We complement convergence result proved [2] using tools from dynamical systems theory. Our proof relies on two principal arguments addition to Picard-like iteration method. First, linearized semigroup is positive allows precisely...

Abstract We consider a system of finite horizon, sequentially interconnected, obliquely reflected backward stochastic differential equations (RBSDEs) with Lipschitz coefficients. show existence solutions to our RBSDEs by applying Picard iteration approach. Uniqueness then follows relating the limit an auxiliary impulse control problem. Moreover, we that solution is connected weak game where one...

Discrete Painlevé equations are studied from various points of view as integrable systems [2], [7]. They are discrete equations which are reduced to the Painlevé differential equations in a suitable limiting process, and moreover, which pass the singularity confinement test. Passing this test can be thought of as a difference version of the Painlevé property. The Painlevé differential equations...

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases,...

The problem of downward continuation of the gravity field from the Earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying Stokes formula is sought in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the Earth’s surface. Downward continuation is a...

The halo orbits around the Earth-Moon L2 libration point provide a great candidate orbit for a lunar communication satellite, where the satellite remains above the horizon on the far side of the Moon being visible from the Earth at all times. Such orbits are generally unstable, and station-keeping strategies are required to control the satellite to remain close to the reference orbit. A recentl...

This paper is concerned with the efficient computation of periodic orbits in large-scale dynamical systems that arise after spatial discretization of partial differential equations (PDEs). A hybrid Newton–Picard scheme based on the shooting method is derived, which in its simplest form is the recursive projection method (RPM) of Shroff and Keller [SIAM J. Numer. Anal., 30 (1993), pp. 1099–1120]...