General Solution of the Three-site Master Equation
نویسنده
چکیده
We first obtain by analogy with the continuous (differential) case the general solution of a discrete Riccati equation. Our results can be considered the discrete analog of Miel-nik's construction in supersymmetric quantum mechanics [J. Moreover, we establish the full equivalence of our discrete Riccati equation and a corresponding homogeneous second order discrete linear equation. We present an application to the three-site master equation obtaining explicitly the general solutions for the simple cases of free random walk and the biased random walk. We consider the continuous Riccati equation (CRE) y ′ = a(x)y 2 + b(x)y + c(x) with the known particular solution y 0 and let y 1 = u + y 0 be the second solution. By substituting y 1
منابع مشابه
General Solution of the Three-site Master Equation and the Discrete Riccati Equation
We first obtain by analogy with the continuous (differential) case the general solution of the discrete Riccati equation. Moreover, we establish the full equivalence between our discrete Riccati equation and a corresponding homogeneous second order discrete linear equation. Our results can be considered the discrete analog of Mielnik's construction in supersymmetric quantum mechanics [J. Math. ...
متن کاملThe Three-step Master Equation: Class of Parametric Stationary Solutions
We examine the three-step master equation from the standpoint of the general solution of the associated discrete Riccati equation. We report by this means stationary master solutions depending on a free constant parameter, denoted by D, that should be negative in order to assure the positivity of the solution. These solutions correspond to different discrete Markov processes characterized by th...
متن کاملOn the Exact Solution for Nonlinear Partial Differential Equations
In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...
متن کاملThree-Step Master Equation: Parametric Stationary Solution
In general, the three-step population master equation is used by physicists in many studies of diffusion processes of microscopic particles on one-dimensional lattices [1], but this simple discrete equation has extensive and interesting applications in other fields as well, most recently to Hubbell’s neutral theory in ecology [2]. In the following, we shall use a population interpretation. It r...
متن کاملPositive solution of non-square fully Fuzzy linear system of equation in general form using least square method
In this paper, we propose the least-squares method for computing the positive solution of a $mtimes n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based on Kaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of ...
متن کامل