| Abstract: |
| In this talk, we discuss methods for computing blow-up solutions of ordinary differential equations in a simple and efficient manner. Broadly speaking, there are two main approaches: one assumes the leading-order term in the asymptotic expansion of blow-up solutions, while the other reduces the problem to the construction of local stable manifolds of bounded invariant sets via compactification of the phase space.
Here we examine algebraic and geometric correspondences of blow-up solutions that enable computer-assisted proofs with reduced validation estimates, while ensuring the existence of solutions with various asymptotic behaviors.
In particular, the correspondence between these approaches provides different types of stability information, offering useful insights for more advanced analysis as well as numerical computation.
This talk focuses on the underlying mathematical framework relevant to computer-assisted proofs and does not address the latest results in computer-assisted validation. |
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