A note on the integral formulation of Kumar and Sloan

In this note, we present a uniform approximation and a methodology for developing a posteriori error estimates for the recently proposed method of Kumar and Sloan. Kumar and Sloan proposed a formulation which converts a Hammerstein equation into a conducive form for approximation by a collocation method. Symbolic computation is used in performing the numerous analytic manipulations leading to the establishment of the error estimates. Finally, some remarks on the generalization of the method of Kumar and Sloan to higher-dimensional systems are offered.