Richardson Extrapolation of Superconvergent Projection-Type Methods for Hammerstein Equations*.

For a nonlinear Hammerstein equation with a smooth kernel, a method proposed recently, based on projection onto a space of piecewise polynomials of degree ≤ r − 1 , is shown to have convergence of order 4 r. This paper shows that this method have asymptotic series expansion and the order of convergence can be further improved to 4 r + 2 by one step of Richardson extrapolation, assuming the calculation to be repeated with each subinterval halved. Some numerical results are given to illustrate this improvement. [ABSTRACT FROM AUTHOR]