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

Allouch, C.; Sbibih, D.; Tahrichi, M.

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.

SUPERCONVERGENT methods; HAMMERSTEIN equations; ASYMPTOTIC expansions; NONLINEAR equations; KERNEL (Mathematics); ORTHOGRAPHIC projection; EXTRAPOLATION

Numerical Functional Analysis & Optimization, 2020, Vol 41, Issue 7, p806

0163-0563

Academic Journal

10.1080/01630563.2019.1704779