Browsing by Author "JUANG, J"

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COMPARISON-THEOREMS FOR THE MATRIX RICCATI EQUATION
(1994-01-01)
JUANG, J
;
LEE, MT
;
交大名義發表
;
應用數學系
;
National Chiao Tung University
We derive comparison theorems for the matrix-valued Riccati equations of the form R(i)'(z) = B(i)(z) + A(i)(z)R(i)(z) + R(i)(z)D(i)(z) + R(i)(z)C(i)(z)R(i)(z), R(i)(0) = R0,i, i = 1, 2. Such equations arise in transport problems and other applications. Sufficient conditions under which R1(z) - R2(z) greater-than-or-equal-to 0 and R1(z) - R2(z) > 0 (in the componentwise sense) for all z are given, respectively. The comparison theorems in which the positivity is defined in terms of positive semidefiniteness were obtained by Royden. Because of the intrinsic disparity in the nature of positivity structure, the techniques developed there cannot be applied to our problem.
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.
EXISTENCE OF ALGEBRAIC MATRIX RICCATI-EQUATIONS ARISING IN TRANSPORT-THEORY
(1995-11-15)
JUANG, J
;
交大名義發表
;
應用數學系
;
National Chiao Tung University
;
Department of Applied Mathematics
We consider the existence of positive 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 cu is an angular shift. Equations of this class are induced via invariant imbedding and the shifted Gauss-Legendre quadrature formula from a simple transport model. By establishing the existence of positive solutions of such equations, the problem of the convergence of some iterative schemes for solving them can be completely solved.
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).
ON COUPLED INTEGRAL H-LIKE EQUATIONS OF CHANDRASEKHAR
(1995-07-01)
JUANG, J
;
交大名義發表
;
應用數學系
;
National Chiao Tung University
;
Department of Applied Mathematics
A recently proposed ''simple transport model'' equation with an ''angular shift'' a (0 less than or equal to alpha less than or equal to 1) leads to a coupled integral H-like equation of Chandrasekhar. Such coupled H-like equations can be treated in terms of a one-parameter (k(1), 0 < k(1) < 1) family. From there an a priori bound can be obtained, which is independent of k(1), alpha, and c (0 less than or equal to c less than or equal to 1). Here c denotes the average total number of particles emerging from a collision. Consequently, we conclude that positive solutions of such coupled integral H-like equations exist. Moreover, we show that such equations have a unique positive solution pair for c = 0 or c = 1 and alpha = 0 or alpha = 1, and that the equations have exactly two positive solution pairs for 0 < c < 1 and 0 less than or equal to alpha < 1 or c = 1 and alpha sufficiently close to 1.