An alternative formulation of the differential quadrature method with a neural network perspective

The differential quadrature method is a well-known numerical approach for solving ordinary and partial differential equations. This work introduces an explicit form for the approximate solution using differential quadrature rules. Analogies with Taylor's expansion are presented. Some properties are formally discussed. An interpretation of the approach from the neural networks perspective is also offered. For a fair comparison, we selected from the literature relevant examples numerically solved by approaches mainly in the realm of Taylor formalism, including a kind of neural network. Compared to the known numerical solutions, the obtained results show the good performance of the method.