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Zbl 1121.65107
Saka, Bülent
Algorithms for numerical solution of the modified equal width wave equation using collocation method. (English)
[J] Math. Comput. Modelling 45, No. 9-10, 1096-1117 (2007). ISSN 0895-7177

Summary: Quintic B-spline collocation algorithms for numerical solution of the modified equal width wave (MEW) equation are proposed. The algorithms are based on Crank-Nicolson formulation for time integration and quintic B-spline functions for space integration. Quintic B-spline collocation method over the finite intervals is also applied to the time split MEW equation and space split MEW equation. Results for the three algorithms are compared by studying the propagation of the solitary wave, interaction of the solitary waves, wave generation and birth of solitons.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
65M06 Finite difference methods (IVP of PDE)
35L75 Nonlinear hyperbolic PDE of higher $(>2)$ order
35Q51 Solitons

Keywords: collocation; solitary waves; quintic B-spline; Crank-Nicolson method in time; numerical examples; modified equal width wave equation; solitons

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