Solution with MATLAB of Sylvester equations from the reflection kernel for a 2D invariant imbedding model of particle transport theory

Seth D.L., . (2003) Solution with MATLAB of Sylvester equations from the reflection kernel for a 2D invariant imbedding model of particle transport theory. [Proceedings Paper]

Invariant imbedding methods have been used to develop alternative mathematical models for particular physical problems that describe the transition of particles or waves from incident to existing states of a physical process. The invariant imbedding method was applied to derive integro-differential equations for transition operators for a two dimensional transport theoretic problem jointly with P. Nelson Texas A anda M University and the late Professor R. Vasudevan Institute of Mathematical Sciences Madras. The general transition operator is composed of four basic transition operators the transmission reflection and the left and right turning operators. The equations for the kernels of the reflection operators are integro-differential equations of Riccati type. The discretized form of this Riccati integro-differential equation reduces to an algebratic Riccati equation that may be reformulated as a Sylvester equation. The Sylvester equation is resolved here in the MATLAB environment on different computational platforms including parallel architecture. The algorithm is presented along with visualizations of the computational results. Results are compared to solutions and timings for an alternate algorithm and by computational plaform.

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Abstract

Invariant imbedding methods have been used to develop alternative mathematical models for particular physical problems that describe the transition of particles or waves from incident to existing states of a physical process. The invariant imbedding method was applied to derive integro-differential equations for transition operators for a two dimensional transport theoretic problem jointly with P. Nelson Texas A anda M University and the late Professor R. Vasudevan Institute of Mathematical Sciences Madras. The general transition operator is composed of four basic transition operators the transmission reflection and the left and right turning operators. The equations for the kernels of the reflection operators are integro-differential equations of Riccati type. The discretized form of this Riccati integro-differential equation reduces to an algebratic Riccati equation that may be reformulated as a Sylvester equation. The Sylvester equation is resolved here in the MATLAB environment on different computational platforms including parallel architecture. The algorithm is presented along with visualizations of the computational results. Results are compared to solutions and timings for an alternate algorithm and by computational plaform.

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Item Type:	Proceedings Paper
AGROVOC Term:	MATHEMATICAL MODELS
AGROVOC Term:	METHODS
AGROVOC Term:	TRANSITION ELEMENTS
AGROVOC Term:	TRANSMISSIONS
AGROVOC Term:	REFLECTOMETRY
AGROVOC Term:	COMPUTER SOFTWARE
AGROVOC Term:	COMPUTER APPLICATIONS
AGROVOC Term:	ANALYTICAL METHODS
AGROVOC Term:	MALAYSIA
Geographical Term:	MALAYSIA
Depositing User:	Ms. Norfaezah Khomsan
Last Modified:	24 Apr 2025 05:27
URI:	http://webagris.upm.edu.my/id/eprint/16280

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