Smoothness and analyticity of $f'=\exp({f^{-1}})$

TL;DR

This paper explores the analytical and numerical properties of the differential equation f' = exp(f^{-1}), presenting new results using RK4 and explicit Runge-Kutta methods to understand its smoothness and analyticity.

Contribution

It introduces new analytical insights and numerical approaches for solving the equation involving the inverse of f, which is a novel focus in this context.

Findings

New analytical results on the equation's properties

Numerical solutions using RK4 and explicit Runge-Kutta methods

Insights into smoothness and analyticity of solutions

Abstract

This paper considers some analytical and numerical aspects of the problem defined by an equation of the type $f'=\exp({f^{-1}})$ with $f^{-1}$ is a composional inverse of $f$,some new analytical and numerical results are presented using RK4 and Explicit Runge kuta methods.