NUMERICAL EVALUATION OF INTEGRALS AND 1-0 SOLUTIONS OF INTEGRAL EQUATIONS

摘要

A method for numerical integration, based on the definition of the Riemann integral, gives approximations for which rigorous error bounds may be obtained automatically, as a result of the computations. The same procedure is extended to integral equations, and it is shown that under certain conditions, the convergence of the approximating procedure guarantees the existence of a solution of the original problem, as well as giving approximate solutions with known error bounds. Applications of this method to linear and nonlinear integral equations are given.