The finite difference (FD) method and the generalised differential quadrature (GDQ) method are numerical techniques grounded in discretising differential equations by approximating derivatives as weighted sums of function values at specific grid points within the solution domain. However, these two methods differ significantly in terms of the number of grid points required to achieve accurate solutions and the precision of the results. The GDQ method has been extensively utilised in engineering problems, such as solving differential equations derived from plate equilibrium equations. Numerous studies have demonstrated its efficiency and accuracy. In comparison to many other numerical methods, GDQ provides greater precision and faster computation. In this paper, a novel, fast, and accurate numerical approach based on the finite difference method is developed to analyse three-dimensional elasticity in plates. This method combines the finite difference method with Lagrange interpolation to create a new algorithm for the analysis of three-dimensional elasticity in plates. A complex test case involving three-dimensional equations, boundary conditions with an elastic foundation, and a material with gradually varying properties has been selected to validate the new method. The results are compared with those from the published literature. The method exhibits remarkable superiority in performance regarding speed and simplicity when compared to the GDQ method. The numerical results illustrate the method's efficiency. It seems that applying the approach used in this study to other numerical methods could also enhance the performance of those methods.
Adineh, M. and Akhavan Ghassabzade, F. (2026). A novel, fast and accurate numerical method for three-dimensional elasticity analysis of plates. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.66564.3119
MLA
Adineh, M. , and Akhavan Ghassabzade, F. . "A novel, fast and accurate numerical method for three-dimensional elasticity analysis of plates", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.66564.3119
HARVARD
Adineh, M., Akhavan Ghassabzade, F. (2026). 'A novel, fast and accurate numerical method for three-dimensional elasticity analysis of plates', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.66564.3119
CHICAGO
M. Adineh and F. Akhavan Ghassabzade, "A novel, fast and accurate numerical method for three-dimensional elasticity analysis of plates," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.66564.3119
VANCOUVER
Adineh, M., Akhavan Ghassabzade, F. A novel, fast and accurate numerical method for three-dimensional elasticity analysis of plates. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.66564.3119
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