Abstract In this work, a three-level implicit compact difference scheme for the generalised form of fourth order parabolic partial differential equation is developed. The discretization is derived by approximating the lower order derivative terms using the governing differential equation with the imbedding technique and is fourth order accurate in space and second order accurate in time. The current approach is advantageous since the boundary conditions are completely satisfied and no further approximations are required to be carried out at the boundaries. The ability of the proposed scheme in handling linear singular problems is examined. The value of first order space derivative is computed alongwith the solution so it does not have to be estimated using the calculated value of the solution. The method successfully works for the highly nonlinear good Boussinesq equation for which more accurate solutions are obtained for the single and the double-soliton solutions in comparison with the existing numerical methods.

中文翻译：

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具有 Dirichlet 和 Neumann 边界条件的四阶抛物线方程的高精度紧凑差分格式：在良好 Boussinesq 方程中的应用

摘要 在这项工作中，提出了四阶抛物线偏微分方程的广义形式的三级隐式紧差分格式。离散化是通过使用带有嵌入技术的控制微分方程逼近低阶微分项来推导出来的，并且在空间上是四阶精确，在时间上是二阶精确的。当前方法是有利的，因为完全满足边界条件并且不需要在边界处执行进一步的近似。检查了所提出的方案在处理线性奇异问题方面的能力。一阶空间导数的值与解一起计算，因此不必使用解的计算值来估计。