
Accession Number : AD0668423
Title : A CAUCHY PROBLEM FOR FREDHOLM INTEGRAL EQUATIONS WITH KERNELS OF THE FORM K1(/TY/) + 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 initialvalue (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 initialvalue 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 differentialintegral 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 differentialintegral 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