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QUINTIC B-SPLINE COLLOCATION METHOD FOR NUMERICAL SOLUTION OF THE RLW EQUATION

Part of: Numerical approximation and computational geometry Partial differential equations, boundary value problems Incompressible inviscid fluids

Published online by Cambridge University Press:  01 January 2008

BÜLENT SAKA ,
İDRIS DAĞ  and
DURSUN IRK
BÜLENT SAKA*
Affiliation:
Mathematics Department, Eskişehir Osmangazi University, 26480 Eskişehir, Turkey (email: bsaka@ogu.edu.tr)
İDRIS DAĞ
Affiliation:
Mathematics Department, Eskişehir Osmangazi University, 26480 Eskişehir, Turkey (email: bsaka@ogu.edu.tr)
DURSUN IRK
Affiliation:
Mathematics Department, Eskişehir Osmangazi University, 26480 Eskişehir, Turkey (email: bsaka@ogu.edu.tr)
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Abstract

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Quintic B-spline collocation schemes for numerical solution of the regularized long wave (RLW) equation have been proposed. The schemes are based on the Crank–Nicolson formulation for time integration and quintic B-spline functions for space integration. The quintic B-spline collocation method over finite intervals is also applied to the time-split RLW equation and space-split RLW equation. After stability analysis is applied to all the schemes, the results of the three algorithms are compared by studying the propagation of the solitary wave, interaction of two solitary waves and wave undulation.

Keywords

RLW equationcollocationsolitary wavesquintic B-splinesundular bore

MSC classification

Secondary: 65D07: Splines 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N35: Spectral, collocation and related methods 76B25: Solitary waves
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 3 , January 2008 , pp. 389 - 410
Copyright
Copyright © Australian Mathematical Society 2008

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