# Accession Number:

## AD0668423

# Title:

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

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1968-04-01

# Pagination or Media Count:

## 20.0

# 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 ut, 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:

# Subject Categories:

- Numerical Mathematics