The extrapolation of Numerovʹs scheme for nonlinear two-point boundary value problems Original Research Article

This paper is concerned with the extrapolation algorithm of Numerovʹs scheme for semilinear and strongly nonlinear two-point boundary value problems. The asymptotic error expansion of the solution of Numerovʹs scheme is obtained. Based on the asymptotic error expansion, Richardsonʹs extrapolation is constructed, and so the accuracy of the numerical solution is greatly increased. Numerical results are presented to demonstrate the efficiency of the extrapolation algorithm.