标题：A new two-level implicit scheme of order two in time and four in space based on half-step spline in compression approximations for unsteady 1D quasi-linear biharmonic equations
摘要：In this article, we discuss a new two-level implicit scheme of order of accuracy two in time and four in space based on the spline in compression approximations for the numerical solution of 1D unsteady quasi-linear biharmonic equations. We use only two half-step points and a central point on a uniform mesh for spline approximations and derivation of the method. The proposed method is derived directly from the continuity condition of the first order derivative of the spline function. For model linear problem, the proposed scheme is shown to be unconditionally stable. The proposed method has successfully tested on the Kuramoto–Sivashinsky equation and extended the Fisher–Kolmogorov equation. From the computational experiment, we obtain better numerical results compared to the results obtained by other researchers.
关键词：Quasi-linear biharmonic equations ; Spline in compression function ; Kuramoto–Sivashinsky equation ; Newton’s iterative method
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