Numerical Algorithms

, Volume 46, Issue 1, pp 45–58

A second order numerical scheme for the solution of the one-dimensional Boussinesq equation

Authors

    • Department of MathematicsTechnological Educational Institution (T.E.I.) of Athens
Original Paper

DOI: 10.1007/s11075-007-9126-y

Cite this article as:
Bratsos, A.G. Numer Algor (2007) 46: 45. doi:10.1007/s11075-007-9126-y

Abstract

A predictor–corrector (P-C) scheme is applied successfully to a nonlinear method arising from the use of rational approximants to the matrix-exponential term in a three-time level recurrence relation. The resulting nonlinear finite-difference scheme, which is analyzed for local truncation error and stability, is solved using a P-C scheme, in which the predictor and the corrector are explicit schemes of order 2. This scheme is accelerated by using a modification (MPC) in which the already evaluated values are used for the corrector. The behaviour of the P-C/MPC schemes is tested numerically on the Boussinesq equation already known from the bibliography free of boundary conditions. The numerical results are derived for both the bad and the good Boussinesq equation and conclusions from the relevant known results are derived.

Keywords

SolitonBoussinesq equationFinite-difference methodPredictor–corrector

Mathematics Subject Classifications (2000)

35Q5135Q5365M0678M2065Y10

Copyright information

© Springer Science+Business Media, LLC. 2007