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A second‐order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation
Author(s) -
Manickam S. Arul Veda,
Pani Amiya K.,
Chung Sang K.
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199811)14:6<695::aid-num1>3.0.co;2-l
Subject(s) - mathematics , monotone cubic interpolation , cubic hermite spline , orthogonal collocation , mathematical analysis , hermite spline , collocation (remote sensing) , thin plate spline , collocation method , spline interpolation , differential equation , computer science , statistics , ordinary differential equation , bilinear interpolation , trilinear interpolation , machine learning , linear interpolation , polynomial
A second‐order splitting method is applied to a KdV‐like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L 2 and L ∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin–Bona–Mahony) and BBMB (Benjamin–Bona–Mahony–Burgers) equations and the well‐known decay estimates are demonstrated for the computed solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 695–716, 1998