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

Abstract

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.

Keywords:

• Differential quadrature rules
• Taylor series-based methods
• systems of ordinary differential equations
• recursive scheme

2020 Maths Classifications:

• 65D99
• 68T99

Acknowledgments

The authors wish to thank the anonymous reviewers and the editor in charge of handling this manuscript for their comments and criticisms. All of their suggestions were followed in the revision of this work. As a result, the final version of this manuscript was greatly improved.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Stefania Tomasiello acknowledges support fromthe European Social Fund via the IT Academy Programme (Institution Project Number SLTAT18445). Jorge E. Macías-Díaz acknowledges financial support from the Consejo Nacional de Ciencia y Tecnologia (CONATY) through [grant number A1-S-45928].