In this work, we present two approaches for simulation of fourth-order parabolic partial differential equations. In the first method, cubic B-spline quasi-interpolation is used to approximate the spatial derivative of the dependent variable and forward difference to approximate the time derivative. In the second method, we have used modified cubic B-spline functions-based differential quadrature method (DQM) for space discretization to get a system of ODEs and then this system is solved by SSP-RK43 method to get the results at knots. The numerical results demonstrate the accuracy of the proposed method. The stability analysis of the methods has also been discussed. It is observed that quasi-interpolation-based method is unconditionally stable, whereas for DQM, the stability has to be checked for a large number of space points. Moreover, for the small number of grid points, DQM gives better results, while for a large number of grid points, quasi-interpolation-based method is better.

在这项工作中，我们提出了两种模拟四阶抛物型偏微分方程的方法。在第一种方法中，三次三次B样条拟插值用于近似因变量的空间导数，正向差则用于近似时间导数。在第二种方法中，我们使用基于改进的三次B样条函数的差分正交方法（DQM）进行空间离散化，得到了一个ODEs系统，然后用SSP-RK43方法对该系统进行求解，以得到结点。数值结果证明了该方法的准确性。还讨论了方法的稳定性分析。可以看出，基于拟插值的方法是无条件稳定的，而对于DQM，必须检查大量空间点的稳定性。此外，