The extrapolation of Numerov's scheme for nonlinear two-point boundary value problems

Authors:
Yuan-Ming Wang
Affiliations:
Department of Mathematics, East China Normal University, Shanghai 200062, People's Republic of China11Corresponding address. and Division of Computational Science, E-Institute of Shanghai Universi ...
Venue:
Applied Numerical Mathematics
Year:
2007

Citing 5
Cited 3

A new fourth-order cubic spline method for second-order nonlinear two-point boundary-value problems

Journal of Computational and Applied Mathematics
Monotone method for diffusion equations with nonlinear diffusion coefficients

Nonlinear Analysis: Theory, Methods & Applications
Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables
Petrov-Galerkin methods for nonlinear systems without monotonicity

Applied Numerical Mathematics
Numerical Methods

Numerical Methods

A fourth-order compact finite difference method for higher-order Lidstone boundary value problems

Computers & Mathematics with Applications
On Numerov's method for a class of strongly nonlinear two-point boundary value problems

Applied Numerical Mathematics
A fourth-order compact finite difference method for nonlinear higher-order multi-point boundary value problems

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper is concerned with the extrapolation algorithm of Numerov's scheme for semilinear and strongly nonlinear two-point boundary value problems. The asymptotic error expansion of the solution of Numerov's scheme is obtained. Based on the asymptotic error expansion, Richardson's 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.