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Numerical validation of blow-up solutions with quasi-homogeneous compactifications

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  1. Article

    Open Access

    Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature

    In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up solutions, are studied. Combining...

    Jean-Philippe Lessard, Kaname Matsue, Akitoshi Takayasu in Journal of Nonlinear Science (2023)

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  2. Article

    Open Access

    Correction to: Rigorous numerics for nonlinear heat equations in the complex plane of time

    Akitoshi Takayasu, Jean-Philippe Lessard, Jonathan Jaquette… in Numerische Mathematik (2022)

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  3. Article

    Open Access

    Rigorous numerics for nonlinear heat equations in the complex plane of time

    In this paper, we introduce a method for computing rigorous local inclusions of solutions of Cauchy problems for nonlinear heat equations for complex time values. The proof is constructive and provides explici...

    Akitoshi Takayasu, Jean-Philippe Lessard, Jonathan Jaquette… in Numerische Mathematik (2022)

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