Numerical study of soliton behavior of generalised Kuramoto-Sivashinsky type equations with Hermite splines
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Date
2025
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Abstract
The traveling wave behavior of the nonlinear third and fourth-order advection-diffusion
equation has been elaborated. In this study, the effect of dispersion and dissipation processes
was mainly analyzed thoroughly. In the thorough analysis, strictly permanent short waves to
breaking waves, having comparative higher amplitudes, have been observed. The governed problem
was employed with the space-splitting method for a coupled system of equations to conduct
the computational process. For the time derivative, the Crank-Nicolson difference approximation
was studied. An orthogonal collocation method using Hermite splines has been implemented to
approximate the solution of the semi-discretized coupled problem. The proposed method reduces
the equation to an iterative scheme of an algebraic system of collocation equations, which reduced
the computational complexity. The proposed scheme is found to be unconditionally stable, and the
numerical demonstrations and comparisons represented the computational efficiency.