Review article

The article deals with the accuracy of approximatesolutions obtained using numerical and analytical methods,namely the Ritz method (used to solve the variationalproblem) and the Bubnov - Galerkin method (used tosolve differential equations). These methods assume thedecomposition of the approximate solution into series overcomplete linearly independent systems. As such systems,this paper compares two commonly used approaches:trigonometric and polynomial bases. A discrepancy is usedto evaluate the accuracy of the solutions obtained. Themathematical model of plate bending Sophie Germain-Lagrange in the variational formulation and in the form of a differential equation of equilibrium is used as an example to show the observed effects.