Accession Number : AD0668423

Title :   A CAUCHY PROBLEM FOR FREDHOLM INTEGRAL EQUATIONS WITH KERNELS OF THE FORM K1(/T-Y/) + K2(T+Y),

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Kagiwada,H. H. ; Kalaba,R. E.

Report Date : APR 1968

Pagination or Media Count : 20

Abstract : The report describes a method for converting Fredholm integral equations with 'spectral' kernels into equivalent initial-value (Cauchy) problems that can be solved effectively by analog or digital computer. In this treatment the upper limit of integration, c, is viewed as an independent variable. An initial-value problem is derived for u(t, c), where u evaluated at a fixed point t is regarded as a function of c. The auxiliary functions R, e, and J, and the function u, satisfy differential-integral equations, subject to initial conditions. In the numerical method, the integrals in the differential equations are approximated by sums according to a quadrature formula. Then the system of differential-integral equations reduces to ordinary differential equations that can easily be solved by a computer. (Author)

Descriptors :   (*INTEGRAL EQUATIONS, *CAUCHY PROBLEM), THERMAL RADIATION, BOUNDARY VALUE PROBLEMS, APPROXIMATION(MATHEMATICS), COMPUTER PROGRAMMING, PROBLEM SOLVING

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE