2015 **Abstract:** Judicious use of interval arithmetic, combined with careful pen and paper estimates, leads to effective strategies for computer assisted analysis of nonlinear operator equations. The method of radii polynomials is an efficient tool for bounding the smallest and largest neighborhoods on which a Newton-like operator associated with a nonlinear equation is a contraction mapping. The method has been used to study solutions of ordinary, partial, and delay differential equations such as equilibria, periodic orbits, …

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“…A proof of this lemma can be found, e.g., in Yamamoto (1998), Day et al (2007) and Hungria et al (2016).…”

confidence: 94%

“…A proof of this lemma can be found, e.g., in Yamamoto (1998), Day et al (2007) and Hungria et al (2016).…”

confidence: 94%

“…The functional analytic setup is close to the one utilized in Hungria et al (2016) with the main difference lying in the convolution structure.…”

confidence: 99%

“…Our method, which builds on foundations laid in [10,11,12,13], is summarized as follows. At the center of the method is an approximate solution u num , obtained through a numerical calculation.…”

confidence: 99%