M\"untz Pseudo Spectral Method: Theory and Numerical Experiments

TL;DR

This paper introduces new non-classical Lagrange basis functions based on Jacobi-M"untz functions, develops associated interpolants, derives error bounds, and demonstrates their effectiveness through numerical experiments.

Contribution

The paper proposes novel non-classical Lagrange basis functions derived from Jacobi-M"untz functions, along with new interpolants and error analysis, advancing spectral methods.

Findings

New basis functions improve spectral approximation accuracy

Derived error bounds validate the interpolants' effectiveness

Numerical experiments confirm computational efficiency

Abstract

This paper presents two new non-classical Lagrange basis functions which are based on the new Jacobi-M\"untz functions presented by the authors recently. These basis functions are, in fact, generalizations form of the newly generated Jacobi based functions. With respect to these non-classical Lagrange basis functions, two non-classical interpolants are introduced and their error bounds are proved in detail. The pseudo-spectral differentiation (and integration) matrices have been extracted in two different manners. Some numerical experiments are provided to show the efficiency and capability of these newly generated non-classical Lagrange basis functions.