Order reductions of Lorentz-Dirac-like equations

We discuss the phenomenon of preacceleration in the light of a method of successive approximations used to construct the physical order reduction of a large class of singular equations. A simple but illustrative physical example is analyzed to get more insight into the convergence properties of the method.Comment: 6 pages, LaTeX, IOP macros, no figure

Solution of Volterra integral equations by method of successive approximations

Bu çalışmada farklı tipte integral denklemler ve onların çözümleriyle ilgili durumlar incelenmiştir. Bu denklemler yaklaşık ardışıklar yöntemiyle çözülmüştür. Bu çalışma dört bölümden oluşur. Birinci bölümde, önceki dönemlerde yapılan çalışmalar ve bu tezde yapılacak olanlar anlatılmıştır. İkinci bölümde ise, gerekli temel tanımlar, Volterra ve Fredholm integral denklemlerin yaklaşık ardışıklar yöntemiyle çözümü üzerinde durulmuştur. Üçüncü bölümde ise, R1, R2, R3 `deki sabit katsayılı dalga denklemlerinin D'alambert, Poisson ve Kirchgoff integral denklemlerine indirgenebileceğine ve bunların çözümleri üzerinde durulmuş, varlık ve teklik teoremleri ispatlanmıştır. Dördüncü bölümde ise fonksiyon katsayılı dalga denklemleri ve bunların çözümleri üzerinde durulmuştur. Beşinci bölümde elde edilen sonuçlar verildi.Different type of integral equations and their solutions are considered in this thesis. These integral equations were solved by the successive approximations. This thesis consists of four chapters. In the first chapter, history of integral equations are given and which were studied. In the second chapter, the basic concepts are given which are necessary for the subject Volterra and Fredholm integral equations were solved by the successive approximations method. In the third chapter, initial value problems for hyperbolic equations with constant confficients in R1, R2, R3 are reducible to D'alambert, Poisson and Krichhoff's integral equations were solved by the successive approximations. The existence and uniqueness theorems for the solution of an integral equations. In the fourth chapter wave equation with the funcion velocity are studied. The existence and uniquenses theorems for the solution of an integral equations. The fifth chapter involves the conclusion of study

Contractivity of the Method of Successive Approximations for Optimal Control

Strongly contracting dynamical systems have numerous properties (e.g., incremental ISS), find widespread applications (e.g., in controls and learning), and their study is receiving increasing attention. This work starts with the simple observation that, given a strongly contracting system, its adjoint dynamical system is also strongly contracting, with the same rate, with respect to the dual norm, under time reversal. As main implication of this dual contractivity, we show that the classic Method of Successive Approximations (MSA), an indirect method in optimal control, is a contraction mapping for short optimization intervals or large contraction rates. Consequently, we establish new convergence conditions for the MSA algorithm, which further imply uniqueness of the optimal control and sufficiency of Pontryagin's minimum principle under additional assumptions

The method of successive approximations for the discounted Markov game

This paper presents a number of successive approximation algorithms for the repeated two-person zero-sum game called Markov game using the criterion of total expected discounted rewards. As Wessels [12] did for Markov decision processes stopping times are introduced in order to simplify the proofs. It is shown that each algorithm provides upper and lower bounds for the value of the game and nearly optimal stationary strategies for both players

A Nonlinear Approximate Solution to the Damped Pendulum Derived Using the Method of Successive Approximations

An approximate analytic solution to the damped pendulum is derived using the method of successive approximations to obtain a nonlinear approximation for the system. We take the approximate solution to the undamped pendulum using the method of successive approximations and compare it to the damped pendulum solution when a linear approximation is used. By looking at these two solutions, we can make an educated guess about the form of the general, approximate solution to the nonlinear damped pendulum. By adjusting the initial guesses and the initial conditions, we derive approximate solutions in three ways. Using MATLAB, the approximate solutions are compared to the full numerical solution through the Euler-Cromer method. To determine how accurate the approximations are, the errors of the approximations are calculated relative to the full numerical Euler-Cromer solution. Each new approximation came with a significant decrease in error, with the final error being 0.0099. This resulted in an improvement to the method of successive approximations. Finally, our best approximation is compared to an available and previously published work

Fokker-Planck Equation with Fractional Coordinate Derivatives

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result, we obtain Fokker-Planck equation with fractional coordinate derivative of order $1<\alpha<2$.Comment: LaTeX, 16 page

Solutions to the Wheeler-Dewitt Equation Inspired by the String Effective Action

The Wheeler-DeWitt equation is derived from the bosonic sector of the heterotic string effective action assuming a toroidal compactification. The spatially closed, higher dimensional Friedmann-Robertson-Walker (FRW) cosmology is investigated and a suitable change of variables rewrites the equation in a canonical form. Real- and imaginary-phase exact solutions are found and a method of successive approximations is employed to find more general power series solutions. The quantum cosmology of the Bianchi IX universe is also investigated and a class of exact solutions is found.Comment: 21 pages of plain LaTeX, Fermilab-Pub-93/100-