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In this work, we propose an efficient computational technique for a recognized three-layer beam model which is described by a third-order linear ordinary differential equation. By using the Mickens' methodology, an exact finite difference (EFD) scheme for this model is constructed. The EFD scheme provides an explicit recurrence formula to compute the solution of the beam model, but it is more efficient than the formula of the exact solution. Moreover, the EFD scheme is also more efficient than well-known standard finite difference schemes in both computational time and accuracy. Finally, two numerical experiments are performed to illustrate the theoretical results as well as to show advantages of the EFD scheme.

An exact finite difference scheme for a three-layer beam model