Numerical solutions for implicit differential equations with singularities

Numerical solutions for implicit differential equations with singularities

Authors

DOI:

https://doi.org/10.5433/1679-0375.2022v43n1Espp3

Keywords:

Implicit differential equations, Singularities, Differential algebraic equations

Abstract

In this paper we introduce a technique to deal with implicit differential equations exhibiting singularities. Our approach is a geometrical one, we use the concept of contact structure on a manifold associated with the differential equation. In this setting we prove an existence and uniqueness theorem. We also show how it relates to known geometric results for this kind of equation. We also indicate how the method can be implemented by using continuation methods techniques and the BDF (Backward Differentiation Formula).

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Author Biographies

Antonio Castelo, Universidade de São Paulo - USP

Prof. Dr. at the Department of Applied Mathematics and Statistics - USP, São Carlos,

Geovan Tavares, Pontifícia Universidade Católica de São Paulo - PUC-SP

Prof. Dr. at the Department of Mathematics, PUC-Rio, Rio de Janeiro

Juliana Bertoco, Universidade de São Paulo - USP

Prof. Dr. at the Department of Applied Mathematics and Statistics - USP, São Carlos

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Published

2022-05-17

How to Cite

Castelo, A., Tavares, G., & Bertoco, J. (2022). Numerical solutions for implicit differential equations with singularities. Semina: Ciências Exatas E Tecnológicas, 43(1Esp), 3–16. https://doi.org/10.5433/1679-0375.2022v43n1Espp3

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