Solving Dym equation using quartic B-spline and quartic trigonometric B-spline collocation methods

Solving Dym equation using quartic B-spline and quartic trigonometric B-spline collocation methods

The nonlinear Dym equation is solved numerically using the quartic B-spline (QuBS) and quartic trigonometric B-spline (QuTBS) collocation methods. The QuBS and QuTBS are utilized as interpolating functions in the spatial dimension while the finite difference method (FDM) is applied to discretize the...

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Hauptverfasser: Anuar, Hanis Safirah Saiful, Mafazi, Nur Hidayah, Hamid, Nur Nadiah Abd, Majid, Ahmad Abd, Azmi, Amirah
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Collocation methods
Finite difference method
Stability analysis
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Mafazi, Nur Hidayah
Hamid, Nur Nadiah Abd
Majid, Ahmad Abd
Azmi, Amirah
description The nonlinear Dym equation is solved numerically using the quartic B-spline (QuBS) and quartic trigonometric B-spline (QuTBS) collocation methods. The QuBS and QuTBS are utilized as interpolating functions in the spatial dimension while the finite difference method (FDM) is applied to discretize the temporal space with the help of theta-weighted method. The nonlinear term in the Dym equation is linearized using Taylor’s expansion. Two schemes are performed on both methods which are Crank-Nicolson and fully implicit. Applying the Von-Neumann stability analysis, these schemes are found to be conditionally stable. Several numerical examples of different forms are discussed and compared in term of errors with exact solutions and results from the FDM.
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subjects Collocation methods
Finite difference method
Stability analysis
title Solving Dym equation using quartic B-spline and quartic trigonometric B-spline collocation methods
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