Numerical Algorithms

, Volume 46, Issue 1, pp 45–58

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

Original Paper


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.


Soliton Boussinesq equation Finite-difference method Predictor–corrector 

Mathematics Subject Classifications (2000)

35Q51 35Q53 65M06 78M20 65Y10 


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© Springer Science+Business Media, LLC. 2007

Authors and Affiliations

  1. 1.Department of MathematicsTechnological Educational Institution (T.E.I.) of AthensAthensGreece

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