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Collocation method using quadratic B-spline for the RLW equation. (English) Zbl 0990.65116

Summary: A collocation method is presented here for the regularized long wave (RLW) equation by using quadratic B-splines at mid points as element shape functions. A linear stability analysis shows the scheme to be unconditionally stable. Test problems, including the migration and interaction of solitary waves, are used to validate the method which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied, and then we prove that the number of solitons which are generated from Maxwellian initial conditions are determined and we compare our results with earlier studies.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q51 Soliton equations
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[1] DOI: 10.1017/S0022112066001678
[2] Abdulloev Kh.O., Phys.Lett. 56 pp 427– (1976)
[3] DOI: 10.1016/0021-9991(77)90088-2 · Zbl 0361.65100
[4] DOI: 10.1016/0021-9991(85)90001-4 · Zbl 0578.65120
[5] DOI: 10.1016/0021-9991(79)90124-4 · Zbl 0407.76014
[6] Wahlbin L., Numer.Math. pp 289– (1975)
[7] DOI: 10.1016/0021-9991(90)90047-5 · Zbl 0717.65072
[8] Prenter P.M., Spline and Variational Methods (1975) · Zbl 0344.65044
[9] Soliman A.A. Numerical Studies for the Regularized Long Wave equation M.Sc.Thesis Menoufia University 1993
[10] DOI: 10.1017/S0305004100055572 · Zbl 0387.35050
[11] DOI: 10.1007/BF02748640
[12] Lewis J.C., Phys.Lett. 73 pp 275– (1979)
[13] Raslan K.R. Numerical Methods For Partial Differential Equations Ph.D.Thesis Al-Azhar Univ. Cairo 1999
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