Browsing by Author "NELSON, P"

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CONVERGENCE-RATES OF ITERATIVE SOLUTIONS OF ALGEBRAIC MATRIX RICCATI-EQUATIONS
(1995-10-01)
JUANG, J
;
NELSON, P
;
應用數學系
;
Department of Applied Mathematics
We consider the iterative solutions of a certain class of algebraic matrix Riccati equations with two parameters, c(0 less than or equal to c less than or equal to 1) and alpha(0 less than or equal to alpha less than or equal to 1). Here c denotes the fraction of scattering per collision and alpha is an angular shift. Equations of this class are induced via invariant imbedding and the shifted Gauss-Lengendre quadrature formula from a ''simple transport model.'' The purpose of this paper is to describe the effects of the parameters c, alpha, and N (the dimension of the matrix) on the convergence rates of the iterative solutions. We also compare the convergence rates of those iterative methods.
CONVERGENCE-RATES OF ITERATIVE SOLUTIONS OF ALGEBRAIC MATRIX RICCATI-EQUATIONS
(1995-10-01)
JUANG, J
;
NELSON, P
;
應用數學系
;
Department of Applied Mathematics
We consider the iterative solutions of a certain class of algebraic matrix Riccati equations with two parameters, c(0 less than or equal to c less than or equal to 1) and alpha(0 less than or equal to alpha less than or equal to 1). Here c denotes the fraction of scattering per collision and alpha is an angular shift. Equations of this class are induced via invariant imbedding and the shifted Gauss-Lengendre quadrature formula from a ''simple transport model.'' The purpose of this paper is to describe the effects of the parameters c, alpha, and N (the dimension of the matrix) on the convergence rates of the iterative solutions. We also compare the convergence rates of those iterative methods.
GLOBAL EXISTENCE, ASYMPTOTICS AND UNIQUENESS FOR THE REFLECTION KERNEL OF THE ANGULARLY SHIFTED TRANSPORT-EQUATION
(1995-03-01)
JUANG, J
;
LIN, HC
;
NELSON, P
;
應用數學系
;
Department of Applied Mathematics
A nonlinear integrodifferential initial value problem, which is induced from a ''simple transport model,'' is investigated. The underlying equation contains two parameters c and alpha. Here c (c greater than or equal to O) denotes the fraction of the scattering per collision and alpha (O less than or equal to alpha less than or equal to 1) is an angular shift. In this paper, we exploit the relationship between the solution in the half space and that in slab geometry. We are thus able to show that the problem has a unique, positive, uniformly bounded and globally defined solution for O less than or equal to c less than or equal to 1 and O less than or equal to alpha less than or equal to 1. Moreover, it is shown that such global solution converges to the minimal positive solution of the half space problem as the spatial variable approaches infinity (i.e. the slab becomes thicker).