Numerical verification method for positiveness of solutions to elliptic equations
Kazuaki Tanaka, Kouta Sekine, and Shin'ichi Oishi
TL;DR
This paper introduces a numerical method to verify the positivity of solutions to semilinear elliptic equations, providing a practical way to confirm solution properties without complex calculations.
Contribution
The paper presents a new numerical verification technique for ensuring solutions to elliptic equations are positive, with a sufficient condition that is easy to check.
Findings
Method successfully verifies positivity in numerical examples
Provides a sufficient condition for solution positivity
Simplifies the verification process for elliptic solutions
Abstract
In this paper, we propose a numerical method for verifying the positiveness of solutions to semilinear elliptic equations. We provide a sufficient condition for a solution to an elliptic equation to be positive in the domain of the equation, which can be checked numerically without requiring a complicated computation. We present some numerical examples.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Numerical Methods and Algorithms · Model Reduction and Neural Networks