Approximate double series solution to certain Fredholm integral equations of the first kind (Q1825018)

The author considers a class of Fredholm integral equations of the first kind with an arbitrary non-degenerate kernel that is twice differentiable in the variable of integration. A new variational discretized-kernel double series solution which may be discontinuous in the other variable is obtained. It is also shown that these solution double series may converge faster than the corresponding Taylor series or Padé approximant. Further, it is shown that they form a basis for a real axis approximate method for the inversion of the Laplace transform.