
Accession Number : AD0668754
Title : INITIALVALUE METHODS FOR INTEGRAL EQUATIONS ARISING IN THEORIES OF THE SOLAR ATMOSPHERE,
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Kagiwada,Harriet ; Kalaba,Robert ; Ueno,Sueo
Report Date : APR 1968
Pagination or Media Count : 25
Abstract : A computationally useful initialvalue theory for determining the intensity of radiation emerging normal to the surface of the atmosphere for comparison with observed profiles is discussed. In this theory the emergent intensity E is the solution of an initialvalue problem in which the independent variable is the interval length, or x, the optical thickness. The solution is determined as the thickness is varied from x equals zero when E equals zero, to x equals the desired thickness value. The computational procedure is based on the ability of modern computers to effectively solve large systems of ordinary differential equations subject to a complete set of initial conditions. The differentialintegral equations of the exact theory are replaced by a system of ordinary differential equations in which the definite integrals are approximated by sums according to a quadrature formula. A suitably chosen quadrature formula can yield a very good approximation. (Author)
Descriptors : (*SOLAR ATMOSPHERE, THERMAL RADIATION), CHROMOSPHERE, BOUNDARY VALUE PROBLEMS, INTEGRAL EQUATIONS, DIFFERENTIAL EQUATIONS, NUMERICAL METHODS AND PROCEDURES, MATHEMATICAL MODELS
Subject Categories : Astrophysics
Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE