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• W2909591775 abstract "Abstract In this work, compact difference scheme based on half-step discretization is proposed to solve fourth order time dependent partial differential equations subject to Dirichlet and Neumann boundary conditions. The difference method reported here is second order accurate in time and fourth order accurate in space. The scheme employs only three grid points at each time-level and the given boundary conditions are exactly satisfied with no further approximations at the boundaries. The linear stability of the presented method has been examined and it is shown that the proposed two-level finite difference method is unconditionally stable for a model linear problem. The developed method is directly applicable to fourth order parabolic partial differential equations with singular coefficients which is the main highlight of our work. The method is successfully tested on singular problem. The proposed method is applied to find the numerical solution of the classical nonlinear Kuramoto–Sivashinsky equation and the extended Fisher–Kolmogorov equation. Comparison of the obtained results with those of some earlier known methods demonstrate the superiority of the present approach." @default.
• W2909591775 created "2019-01-25" @default.
• W2909591775 creator A5020864940 @default.
• W2909591775 creator A5043230408 @default.
• W2909591775 date "2019-05-01" @default.
• W2909591775 modified "2023-09-26" @default.
• W2909591775 title "Two-level implicit high order method based on half-step discretization for 1D unsteady biharmonic problems of first kind" @default.
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• W2909591775 doi "https://doi.org/10.1016/j.apnum.2018.12.015" @default.
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