Derivation matrix in mechanics – data approach

Existence of data allows use solution methods for differential equations that would otherwise be inapplicable. The process this is formalized by using derivation matrices reduce the time necessary and solving equations. Derivation are formulated applying numerical in matrix notation, like finite difference schemes. In work, a novel formulation developed based on Lagrange polynomials with special care taken at boundary points order to persevere uniform precision. main advantage approach straightforward formulation, clear engineering insight into (almost) arbitrary precision through choice interpolation order. result procedure dimension [n×n], where 'n' number points. resulting singular (of rank 'n-1') until boundary/initial conditions introduced. However, does not prevent user successfully differentiate its unknown function represented recorded easily applicable wide range problems. This methodology could extended dynamic systems multiple degrees freedom adapted when velocities or accelerations instead displacements.