... of the elastic thin rectangular plate can be derived through differentiation. However, due to the complexity of boundary conditions, obtaining analytical solutions is extremely challenging. A more practical approach is to employ numerical methods, among which the finite difference method is commonly used (Nguyen...

... of circular nanoplate are investigated. Design/methodology/approach The hybrid differential transformation method (DTM) and finite difference method (FDM) are used to approach the model. The DTM was first applied to the equation with respect to the time, and then the FDM was applied with respect...

...), enabling the present methodology to be robust and accurate. To overcome the difficulty in evaluating the sensitivities of objective and/or constraint functions by analytic method in some cases, the authors adopt the finite difference method to calculate these sensitivities, thereby providing a universal...

.../methodology/approach The filtered three-dimensional non-stationary Navier–Stokes equation is used for simulating the turbulent process. The problem is solved using hybrid methods, where the equation of motion is solved using finite difference methods in combination with cyclic penta-diagonal matrix, which...

...-value problems (IVPs) using numerical methods like finite difference method leads to step by step and time-consuming recursive solutions. Design/methodology/approach – The present method is based on converting the IVP into boundary-value problems (BVPs) and utilizing the features of the latter...