Numerical simulation of the wave (shock profile) propagation of the Kuramoto-Sivanshinky equation using an adaptive mesh method
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In this dissertation we solve the Kuramoto-Sivanshinsky equation numerically using an adaptive mesh method. Discretization in time is done using Crank- Nicolson with septic Hermite collocation method applied in space on an adaptive mesh. The adaptive mesh is a solution of moving mesh partial differential equations derived from the principle of equidistribution. A rezoning approach which works with a decoupled solution procedure is then used to develop a matlab code to produce the numerical results. The method is evaluated for effectiveness and computational efficiency with the most current best method available in the literature.
adaptive mesh method
septic Hermite collocation method