Rigorous numerical enclosures for positive solutions of Lane-Emden's equation with sub-square exponents

2016/07/15 by Kazuaki Tanaka, Tanaka, Kazuaki, Michael Plum +7
Mathematics · #Differential Equations and Boundary Problems #Numerical methods for differential equations #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.1607.04619

Abstract

The purpose of this paper is to obtain rigorous numerical enclosures for solutions of Lane-Emden's equation -Δu=|u|^p-1 u with homogeneous Dirichlet boundary conditions. We prove the existence of a nondegenerate solution u nearby a numerically computed approximation u together with an explicit error bound, i.e., a bound for the difference between u and u. In particular, we focus on the sub-square case in which 1

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