This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic di↵erential equations with random coe cients. Similar to Gao & Liu [19], this extends the corresponding results collected in Freidlin & Wentzell [18]. However, we use a di↵erent line of argument, adapting the PDE method of Fleming [14] and Evans & Ishii [10] to the pathdependent case, by using b...

The dissertation is divided into two separate parts. First part We propose an e cient and generic algorithm for rigorous integration forward in time of systems of equations originating from partial di erential equations written in the Fourier basis. By rigorous integration we mean a procedure, which operates on sets, and return sets which are guaranteed to contain the exact solution. The algori...

In this paper, we are concerned with a class of nonlinear implicit fractional di?erential equation adiscrete delay. By means the contraction mapping principle, prove existence unique solution.Then, investigate continuous dependence solution upon initial delay data and Ulamstability.

A neural network based optimal control synthesis approach is presented for systems modeled by partial di!erential equations. The problem is formulated via discrete dynamic programming and the necessary conditions of optimality are derived. For synthesis of the controller, we propose two sets of neural networks: the set of action networks captures the mapping between the state and control, while...

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...

1. Preliminaries. Multigrid methods originated earlier this century, in the personnel computing era. Someone who needed to compute an approximation to the solution of a partial di erential equation during that era would ll a room with people. After using very simple mechanical calculators to compute parts of the approximation, these people would pass their parts to the other people in the room ...

The goal of this paper is to prove a convergence rate for WongZakai approximations of semilinear stochastic partial di erential equations driven by a nite dimensional Brownian motion.

Applying 3D di erential operators to extract point landmarks from medical images generally su ers from false detections. A considerable number of these false detections is caused by neighboring structures that are included in the region-of-interest (ROI) speci ed by the observer. The main contributions of this paper are two di erent approaches to reducing false detections resulting from neighbo...

We present a novel approach for numerical simulation of uid ow and sediment transport past evolutionary landforms, with emphasis on sand dunes developing in extreme winds. Time-dependent curvilinear coordinates are employed to fully couple ow aloft with the developing landform. The conservation law that de nes shape of the lower boundary depends on details of local surface stress, thereby favou...

We present a Neumann-subproblem a posteriori "nite element procedure for the e$cient and accurate calculation of rigorous, `constant-freea upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial di!erential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori "nite element procedure is described; the asymp...