AN INITIAL-VALUE METHOD FOR GENERAL FREDHOLM INTEGRAL EQUATIONS,

A new analytical and numerical solution of Fredholm integral equations is presented that is not limited, as previously, to equations whose kernels depend on the absolute value of the difference of the arguments. The solution of a Fredholm integral equation at a fixed point is viewed as a function of the length of the interval. An initial-value problem for the solution and for certain auxiliary quantities is then derived an extension of invariant imbedding, and a number of new equations are developed that are well suited for solution by modern computers. This procedure for the computation of the solution is also of analytic interest it has been tested and found to be effective in dealing with equations of radiative transfer.