Chebyshev interpolation for rigorous integrator of differential equations

ReCAP 2022 (Mar.13 - 18)

Akitoshi Takayasu (University of Tsukuba)
Chebyshev interpolation for rigorous integrator of differential equations

Abstract:
In this talk we consider the Chebyshev interpolation in particular for rigorous integrator of differential equations. Generally, to implement the Chebyshev interpolation, the number of Chebyshev polynomials that provides a sufficient approximation of the function depends on the original function to be approximated, and it is not obvious to determine the appropriate number of polynomials. We implement a heuristic algorithm to determine the appropriate number of polynomials and to interpolate the function with good accuracy. As an application, we introduce rigorous integration for the Cauchy problem of differential equations.