new derivation of the integro-differential equations for Chandrasekhar"s X and Y functions

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Published **1964**
by Rand Corporation in Santa Monica, Calif .

Written in English

- Radiative transfer.

**Edition Notes**

Includes bibliography.

Statement | by R. Bellman ... [et al.]. |

Series | Research memorandum -- RM-4349, Research memorandum (Rand Corporation) -- RM-4349.. |

The Physical Object | |
---|---|

Pagination | 8 p. ; |

ID Numbers | |

Open Library | OL17984321M |

Y functions for i = 0 Numerical results for Chandrasekhar's X and Y functions of radiative transfer 1.o 10 m 10 L 90 60 30 0 Arc cos fa (deg) FIG. Y functions for ~ = 0~1. RICHARD BELLMAN, HARRIET KAGIWADA, ROBERT KALABA AND SUI:O UENO by: 9. Solving Integro-Differential Equations. An "integro-differential equation" is an equation that involves both integrals and derivatives of an unknown function. Using the Laplace transform of integrals and derivatives, an integro-differential equation can be solved. Wolfram Language Revolutionary knowledge-based programming language. Wolfram Cloud Central infrastructure for Wolfram's cloud products & services. Wolfram Science Technology-enabling science of the computational universe. Ordinary integro-differential equations are of interest e.g. in population dynamics (). Also, partial integro-differential equations, i.e., equations for functions of several variables which appear as arguments both of integral and of partial differential operators, are of interest e.g. in continuum mechanics (,). References.

This comprehensive work presents a unified framework to investigate the fundamental existence of theory, treats stability theory in terms of Lyapunov functions and functionals, develops the theory of integro-differential equations with impulse effects, and deals with linear evolution equations in abstract by: equations of X- and Y- equations combining the method of Chandrasekhar and Elbert [3] and a method based on iterative solution of Schwarzschild-Milne integral equation. Sobouti [8] tabulated the X- and Y- functions for different values of optical : Rabindra Nath Das. The purpose of this paper is to propose a method for studying integro-differential equations with infinite limits of integration. The main idea of this method is to reduce integro-differential equations to auxiliary systems of ordinary differential equations. Results: a scheme of the reduction of integro-differential equations with infinite limits of integration to these auxiliary Cited by: 2. A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability .

A graphical presentation of the numerical results for Chandrasekhar's X and Y functions of radiative transfer, covering wide ranges of slab thicknesses and albedos for single scattering. The tables on which the graphs are based are obtained by numerically integrating the integro-differential equations satisfied by the X and Y functions. 36 by: This unique monograph investigates the theory and applications of Volterra integro-differential equations. Whilst covering the basic theory behind these equations it also studies their qualitative properties and discusses a large number of applications. This comprehensive work presents a unified framework to investigate the fundamental existence of theory, treats stability theory in . This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction. In atmospheric radiation, Chandrasekhar's X- and Y-function appears as the solutions of problems involving diffusive reflection and transmission, introduced by the Indian American astrophysicist Subrahmanyan Chandrasekhar.

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